My wife is very angry. I always go to her house empty-handed and then go back to my house with big bags. Is my wife too melodramatic, or do I treat my wife's family as my own?

It really is too much of you. It is obviously inappropriate to go to the mother-in-law's house empty-handed. If you really regard her home as your home, then your mother-in-law and father-in-law should do something for her birthday! Father's Day and Mother's Day should also be expressed! Nothing, then how can you say that you treat them as relatives and family! On the contrary, your parents-in-law are very close to you, so they all come back with big bags.