As with the vehicles, the nature of each weapon sometimes makes it more or less suitable for players on slow connections. Again, in increasing order of utility:
Needler
This weapon is fairly useless in multiplayer anyway, barely better than the plasma pistol which is the default weapon on many maps. One good thing about it: the projectiles track, like the plasma pistol's secondary fire, meaning accuracy is not as important as with other weapons. However, the projectiles are slow and relatively easy to dodge or take cover from. If you're toe-to-toe with a single opponent, you might as well melee him with it, it'll do about as much good. If you're in a group with multiple targets, in can do damage, as your opponents won't be able to give their full attention to the miniscule threat you pose.
Sniper Rifle
If you're badly lagged and trying to hit someone with a sniper rifle, you'd better hope they're standing still-- because that's going to be your only chance. Most likely you're also standing more or less still while sniping; but if not, you may find yourself "warping" while zoomed in at 10x and having difficulty keeping your quarry in the crosshairs. Probably the only players you've got a chance at killing this way are either standing still with their backs to you (teammates, perhaps?) or other snipers, in which case they're probably going to react more quickly and kill you before you get off a shot (this happens a lot in the upper base lofts on Sidewinder).
Add to that the small clips and long reload time, and you've got a nightmare for high ping players unless you're very well hidden.
Pistol
Most good players consider this the most powerful weapon in the game, and it usually is. In the right hands, even a player with full shields and health can be dropped to the ground with three accurate headshots.
The problem is, if you've got a lot of lag, getting those three headshots is probably going to use up your clip.
However, as a medium-range weapon the pistol can still be useful because of its scope (the sniper really isn't good for anything but long range for a high ping player, as closer in the "warp" effect plus player movement is going to keep you from drawing a bead on them). However, I suggest going for body shots to make every bullet count, rather than trying for head shots and a quick kill.
Rocket Launcher
Similar to the Scorpion's primary fire cannon, the rocket launcher can do damage in a large radius, so just getting a hit on a vehicle or on the floor or walls near a player can sometimes be enough. However, ammo can be scarce and the reload time is long. However, also like the cannon, you only need to line up your shot once; at close or medium range, most targets will only need one hit (overshield not withstanding).
One word of caution: the scourge of bunny-hopping plagues Halo just as it has previous online games. It is quite common to see players constantly bounding across the landscape. And it seems the preferred weapon of the bunny hopper is the rocket launcher; perhaps because it affects the aim of this weapon less.
It's also damn hard to hit rocket-launching bunny-hoppers while you're lagged; anticipating the rhythm of hops can go awry when you hit a spot of lag; also, if you hit the ground underneath a hopping player with a rocket, it appears to do little or no damage. In addition, an old feature from the Marathon days is back-- jumping players move faster than running ones.
One more aside on bunny-hopping: as if you couldn't tell, this technique, if you want to call it that, really eats my lunch. Please, somebody, put an anti-bunny-hopping feature in. If they can stop the plasma pistol from automatically firing when you hold down the trigger, they can do the same for jumping. Put in a delay as well; after 2 or 3 jumps in the space of a couple of seconds, disallow jumping again for two or three seconds. I'm not one of those guys who are nuts about realism in video game battle tactics, but a server full of bunny-hopping Master Chiefs just looks silly, it's almost demeaning to the character. About the only thing sillier ever seen in Halo were the circle-strafing marines in the E3 2000 trailer video, which I'm personally convinced was the real reason behind the switch to first person perspective. (Notice the marines in single player don't strafe, at least not the way most human players do.)
The downside for the lagged player: long reload time and massive splash damage; in close quarters you can end up suiciding very easily if you fire at just the wrong second.
Plasma Pistol/Plasma Rifle
Both these weapons can allow a HPB to exact a modicum of revenge, as the effect it causes-- slowing players down-- can make them feel like they are the ones that are lagged. You can get a decent rate of primary fire down with each, and the pistol's secondary fire tracks, meaning you only have to fire when the reticle is red to have a decent chance at getting a hit.
Assault Rifle
Like the LAAG guns, the AR lets you fire almost constantly, making it decent at close to medium range, although it does quite a bit less damage. Grab this if you can't get anything else. It virtually is a scanhit weapon, but at medium range while autofiring its accuracy is pretty low. Useful for finishing off targets after you've softened them up with a grenade.
Shotgun
In close quarters, the shotgun is about as effective for all players regardless of connection speed; it's a scanhit weapon (it hits instantly) so leading your target is much less of an issue. It does a fair amount of damage. Especially good for chasing opposing flag-carriers.
Fuel Rod Gun (FRG)
Like the Banshee's secondary fire, but with a higher rate of fire. If you can manage to account for the arc of the projectile and it's rather slow speed, this can be a good weapon for the lagged. It does damage in a decent radius, and is less dangerous to you in close quarters
Flamethrower
The flamethrower is your friend if you're a high ping bastard; seek it out, cradle it lovingly, and feed it napalm. It fires constantly until it runs out and deals out massive amounts of damage at short range.
The thing to be careful about: don't run forward while you use it; you'll run into your own flames before you see them on-screen if you have a lot of lag, and before you even know what's happened, you'll be dead.
Grenades
I'm going to comment on grenades separately from the rest of the weapons, and only in terms of how lag seems to affect them.
Plasma Grenades
Getting a "stick" with a plasma grenade at anything other than extreme close quarters is difficult while lagged unless your target is motionless with their back to you, or if it is a stationary or turning vehicle. Against personnel, you have to account both for the arc and leading your target, which is difficult at best. As plasma grenades don't bounce around that much after throwing if you don't hit the target, they are less useful than frag grenades for doing radius damage in close quarters.
Another note: If you're on a slow connection and you have a slow computer or one with a subpar graphics cards, you may find plasma grenades hard to use. With certain settings, I've seen games in which plasma grenades are almost completely invisible when thrown, and others in which they don't glow at all (I think this happens when you turn particles off). It can be difficult to see where you've thrown under these circumstances, as the little blue suckers can be harder to see against many backgrounds than the olive drab of the frag grenade.
Frag Grenades
Frag grenades are pretty good even when you're lagged; you can lob them quickly, pick them up quickly (if they are nearby) and do damage in a wide radius, especially in confined spaces. Unless there's a high risk of incurring friendly fire, I recommend lobbing them at opponents two at a time just before you think you might die (which happens a lot to the lagged). You can get a lot of dead-man kills this way; you just have to anticipate the moment a little further ahead than other players.