Despite being a weightlifter for ten years before starting Aikido, I want to second the recommendation that Erik H. gave. I have done all the Stew Smith SEAL programs. I can assure you that weight training would have been redundant if you can make it through those programs. I think I should point out that the two trainings (PT versus free weights) prepare your muscles in different ways. Although I maxed out at over 600 pushups, I doubt my benchpress was impressive.
I think the reason why so many discourage "muscle building" in Aikido is because there is a tendency for people not to give equal thoughtfulness to stretching/flexibility/relaxation. The power and/or explosive contractions of weight training don't translate well into ki no nagare techniques. Not all people are like this, of course. But many people in my dojo (myself included) have failed to create a good balance b/n strength building and relaxed flexibility, making their movements jerky, positioning stiff and joints virtually immobile. I believe the combination can be done correctly, but I don't personally know how.