Is it normal for your weimaraner to want to eat a bird after it kills it?

Of course. They are born to be wild, just like anything else. So.. in the wild the Weim would have killed a bird and ate it for a meal. That instinct is still very strong.

P.S. Wouldn't be a bad thing to let him/her eat it. Why not? It's natural for them. Don't worry about the bones either... wild dogs survive by eating wild birds and animals. They will not choke on raw bones.. just cooked ones. NEVER give them cooked bones.