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
Aikido training should never be about physical muscle driven strength. Thats low, low level. Approaching aikido that way will slow down any real progress. The power is in relaxation yes. But it is in "using" that relaxation to both do things and allow things in your body to create aiki.