Baited – lured to a trap with the promise of a reward, or the act of having placed that reward in the trap.
Bated – diminished, reduced, basically the same thing as “abated.”
So if we baited the trap with cheese, then everything about the rat is bated – its life is bated, our rat problem is bated, and its breath is definitely bated. Yes, folks, it’s “waiting with bated breath” not baited. (And not “weighting,” for that matter.) It means to hold your breath in excited anticipation, it doesn’t mean your breath smells like cheese. Though you still might consider a mint now and then, for reals.