So, as per D&D 5E rules, a small character has disadvantage when using a heavy weapon to attack. As DM, would there be some condition I could come up with, to allow a small character to wield a heavy weapon normally? It'd offer funny roleplaying options... Maybe a STR threshold (as in, as long as he has 18 or more)? Maybe giving up a class feature or making up a new background to enable this?
In the interests of maintaining game balance, I'd recommend that you make it a feat. The PHB covers some optional feats you can use (page 165). The idea here is that players can optionally replace the act of increasing ability scores when they hit certain character levels and take a feat instead. You could create a homebrew feat or modify an existing one to allow for this behavior. If they want the ability at level 1, then you could have them sacrifice their racial ability bonuses to take the feat instead.
A good candidate for modifying an existing homebrew feat would be Massive Weapon Fighter. You could modify it so that, in addition to allowing Medium creatures to use over-sized weapons without disadvantage, it allows Small creatures to use heavy weapons without disadvantage. In the interest of balance, I'd take the part about granting a +2 damage with heavy weapons that aren't oversized and amend it to only apply to Medium creatures. You could, however give Small creatures a +2 to damage when using weapons that aren't heavy or oversized.