In B/X, halflings are much like fighters, but with a slew of minor changes that seem geared to make them good ranged combatants. On the one hand, they get a bonus to hit with missile weapons, an initiative bonus and an Armor Class bonus against larger than man-sized creatures. On the other hand, they can only use weapons “cut down to their size” (limiting their offense in melee) and they use six-sided Hit Dice instead of the fighter’s eight-sided dice, making them more fragile than their human and dwarven counterparts.
But in actual play? It’s all frontline halflings in plate mail, all the time.
The reason for this is an emergent property of the B/X rules for ability score adjustment (p. B6). Characters can drop points from some stats to raise a prime requisite on a 2-for-1 basis. And who has Dexterity as a prime requisite? Halflings. So everyone who plays a halfling trades away Intelligence and Wisdom to get an 18 Dexterity, which is impressive when a natural Dexterity score is rarely higher than 15. Combine that with plate mail and shield and you’ve got a base Armor Class of -1, which goes up to -3 against larger than man-sized creatures. The resulting survivability boost more than makes up for having one less hit point per level than the fighter.
The first question here isn’t what’s to be done, but whether anything should be done at all. Is there anything fundamentally wrong with a party with a bunch of plate-armored hobbits anchoring the front line? If the players seem happy enough with the situation, it may be best to let them keep doing what they’re doing.
On the other hand, if the DM’s dissatisfied with the resulting flavor, there are a number of approaches to be taken:
1) Disallow ability score adjustment, so halfling PCs are stuck with their initial dexterity roll. The downsides here are that this may be a case of taking out a housefly with a hand grenade if it’s the only problematic situation caused by ability score adjustment, and that a player who rolled a high dexterity can still choose to play a plate-armored halfling anyway; this makes the situation rarer but does not abolish it.
2) Put a limit on how much of a dexterity bonus a PC can get from heavy armor, like in later editions of D&D. So plate mail might cap the wearer at a +2 (or even +1) AC bonus from dexterity. This meshes well with the movement rules; if metal armor slows you down, it’s reasonable to think that it also makes you less agile in combat.
3) Remove plate mail from the halfling’s list of allowed armor types. This may have an overly negative effect on the halfling’s survivability, and unlike some other solutions, it requires grandfathering in exceptions to the rule for existing characters if you want to let them keep playing as they have been playing. But it has the advantage of matching the race’s original Tolkienian flavor; they’re not the sort to dress up like knights in full armor.