The best I've come up with is to replace scaling damage dice with a flat +1 damage bonus for large weapons. In other words, a large-sized longsword would deal 1d8+1 damage.
IMO, the major reason that using large races is discouraged is that large-sized weapons offer an unreasonable advantage when using attacks with multiple [w] dice (due to scaling). There are other issues to deal with when considering large races (reach, big space, not being able to follow the rest of the party through a kobold bolt hole, etc.) but weapon dice seem to be the main prohibitive factor.
You could similarly expand weapon choices for small races by allowing them to wield small-sized versions of otherwise unusable weapons (a halfling-sized greatsword) at a -1 penalty to damage rolls (1d10-1).
I haven't actually tested this in play; it's just part of a house rules document I've been putting together for fun.