Thanks for comments.
I think I am holding too much back against these players and should - like you say - avoid the river problem by pushing on the flop or turn.
I tend to think that "no one in their right mind would bet that much with only middle pair or a weak kicker - he must hold a set or two pair," when I get raised with AK on a Kxx flop. Maybe I should be a bit braver and push more.

I have the bank roll, but I can't hit back with more then max buy in until I build a larger stack at the table. With this guy I kept refilling to max stack to hit him hard when possible, but never got the cards for it after my 777 hand. I must admit that his showdowns with really strong hands, taking others stacks, made me avoid taking him on. I tightened up to 21% flop and waited. One problem was that he would ruin my games against others. I couldn't get as many preflop/flop small pots as usual due to his aggressive play. Anyway, I'll be better prepared next time