uhh yes he does train with weights. he trains with kettlebells, light dumbbells, and lots of body weight
That's hardly 'weight training'. I havent seen him using light dumbbells, but kettlebells are not really that heavy.
In fact, the man himself says that weights are not necessary for MMA. He lifted while he was in the army and got very strong and he said that they were not necessary after that.
Body weight is not weight training in my opinion, as i'm sure it is in many others.