In one of the original trailers, Elizabeth conjured a storm cloud, which Booker then electrified to damage everyone nearby. Afterward, Elizabeth was exhausted.
Shortly after seeing that, I remember reading a developer preview article which said that too much use of Elizabeth's tears would start to weaken her.
Right now, I've just finished the Hall of Heroes and I haven't seen any evidence of that at all. In the past few combat sequences, there's been just tons of things that I can ask Elizabeth to conjure up for me - mechanical patriots, barrels of guns, health kits, machine gun turrets, and so on.
I haven't taken advantage of many of these (only the first time when she offered to pull through some cargo hooks or a heavy machine gun turret and a couple of health packs since) because I don't want to hurt her. So far, I haven't seen any evidence of damage, but now some of these fights are getting tough without her help.
Will Elizabeth warn me if I start to use her powers in combat too much, or will she just suffer silently?