I train with free weights and dumbells and my bench, doing lots of reps rather than lots of weight -- but I have been able to increase the weight over the months I've been working at it. I was a 125-pound weakling two years ago, but the intense exercise in karate class got me in good enough shape so I don't fall apart in aikido.
In aikido, I find it's hard to do some moves because I lack arm and hand strength -- no, I'm not trying to muscle my techniques, but I can't even turn some of the big guys' wrists in kotegaeshi and my arm gives too much in irimi nage. So I've been concentrating on strengthening my hands and arms. Still doing the intense aerobic karate exercise and jujitsu classes to improve my speed, stamina and overall strength, and doing assorted other exercises to make my back stronger so my ribs stay put during ukemi.
I haven't yet discovered any exercise that hurts my aikido; but then again, I'm so far from "musclebound" that maybe it just can't be an issue for me yet.