@Perrin & @Reinfeld - one of the optimized usage of Balance is usually on the highest DPS, but if OP isn't parsing, there's no way for them to know that. It is also optimal to give a Balance card to a DPS currently in a burst window to also maximize the potential gain from it (e.g., a BRD in a Raging Strikes+Dragon Sight window, or a MNK during their burst window). But that's for an entirely different level of play compared to leveling.

If you know who the highest DPS is, sure, give them the Balance. But if you don't, pass them around.

One situation you could put them to use towards in 4-man content is AOE situations. Say you have a SMN in your group or a BLM; they have monstrous AOE, so they will make good use of a Balance during a large trash pull or two compared to a job with weaker AOE potential (or compared to a DPS that is allergic to their AOE buttons).