Weight training as in power lifitng or isolated body sculpting lifting?
They really are two different things
Dead lifting can be done for whole body strength without that isolated "Hey ma look at my biceps!" thing.
But power lifing, and stretching-which need to go hand in hand-won't help your aikido one wit. May even harm it. I tried it
Tried what, exactly? Powerlifting? Powerlifting is a sport wherein the goal is to deadlift, squat, and bench the most weight possible. As with any sport that involves cultivating extreme attributes, excelling at it will naturally keep you from excelling at certain other activities. No world-class powerlifter will ever be a competitive marathon runner for instance, nor vice-versa.
What you described above seemed to imply that powerlifting and bodybuilding are the only types of weight training. The professional athletes I mentioned do not do either (except powerlifters). Instead they do weight programs designed to provide a base of fitness and injury resistance, and usually have added elements specifically designed to help them with their sport. These elements might be specific movements that are similar to sport movements, or might be ballistic or explosive movements designed to enhance speed and power. They also usually do endurance exercises to provide a base, with added elements that address the energy needs of their sport, variously empsizing aerobic and anaerobic elements. Unless you hired Olympic or pro-team level trainers to design and administer a program for you based on your needs, I seriously doubt you "tried it" and have a legitimate experiential basis for dismissing "it".
However, this was not the subject of the thread. The orginal question was not about how or whether weight training would take one's Aikido to some rarified level. In my view, it probably wouldn't help much in this respect, because that is all about skill, and there are no clearly defined performance goals to even test whether such a program works. The question was about "stiffness" and flexibility, and whether weight training might cause it and thereby hinder one's Aikido. The answer is clearly no, as most pro athletes do employ weight training and there are plenty of examples of these that are way more flexible, finely coordinated, and fluidly moving than most Aikidoists. I have yet to see anything on a mat that compares to Micheal Jordan threading four defenders like they were standing still and finishing with a dunk - all the while relaxed enough to have his tounge sticking out.
I also added that weight training can have several health and injury prevention benefits. In my experience, many Aikidoists are in poor shape, have many injury problems, and often trouble keeping up their energy and wind through a single, moderately vigorous class. Basic fitness training, including a few compound weight exercises could definitely help these people.