RE: Weights are having an adverse affect...
How soon after the workout did you try to draw your bow? I've had times when I fried my triceps and literally couldn't draw my bow for several hours afterward. Muscle fatigue and recovery is a funny thing. I bet if you tried to draw your bow after several days rest you would feel noticeably stronger.
Working out your muscles that you shoot with are not difficult. Anything that creates the pushing/pulling action of the upper body will do this. You just have to make sure you get the "pull" not just the push. Everybody loves the bench press and push-ups but the "pulling" or back exercises are equally important. Seated back pulls, hanging back pulls, lats, etc., are great for increasing strength in your shooting muscles.