Yeah I agree with you to some point, we could make somewhat accurate guess of his range if we knew exactly his flat to minraise range and then his lead on the flop,etc.
I would still bet turn 50-60 so we keep initiative and if he calls we are beat most of the time and I'm not calling a shove either. IMO it's not good to check back turn, because he will bet river with any 2 after your check if he is a fish. If he donked with 35, 57, 58 or 78 it has us beat now. I'm not sure about river, because I don't know his range. It is a sign of weakness imo, but it could be for value too. I think folding is better readless, but clearly he is a fish so call and write down with what hand he was doing that.
Board: 6
4
J
*7
*2
*******Equity*****Win*****Tie
SB*****37.72%**37.13%***0.60%*{ 8s6s }
BB*****62.28%**61.68%***0.60%*{ K6s, K4s, Q6s, Q4s, J5s+, T6s, 96s, 84s+, 74s+, 64s+, 53s+, K4o, Q6o, Q4o, J6o+, T8o+, T6o, 98o, 96o, 87o }