Some class and race features allow a character to "count as one size larger when determining your carrying capacity and the weight you can push, drag, or lift." (Eberron warforged Juggernaut) or "Your carrying capacity (including maximum load and maximum lift) is doubled, and you have advantage on Strength checks made to push, pull, lift, or break objects." (barbarian path of the totem bear)
Would these characters be able to wield a two-handed weapon (eg maul) with one hand? Alternatively, can a larger version of a one-handed weapon be used to give more damage? This seems to work for the "enlarge" spell, so could it work through non-magical means?