I like the play on the flop, builds the pot but doesn't scare him off. If he has a high PP , he may sense a smaller PP like 1010 or JJ or may be looking to fill up a flush draw (if 2 of same suit on flop). We don't know if his flop bet is a standard C-bet since he raised preflop but the fact he calls your raise indicates it likely wasn''t and he is calling with some high PP.
Others liked the turn check, I agree. It's nice, if he somehow hit a set and filled up (unlikely) or made a flush you;'ve got him pretty hooked. And if not hey he's still along for the ride and if he hits a set to fill up a FH on river you're getting paid off.
River comes and Fred checks. This can be thought about 2 ways. One way is to think "whose trapping who." Is it likely Fred had 66 or 88 or 99, not really. It's more likely Fred has something like AA to 1010 (or even some AK that whiffed). His river check either means he thinks he;s trapping a smaller PP with his high PP or second way to consider it, he whiffed OR knows he's behind and looking for a cheap value call to see if his PP is good or not.
All this said I bet about 1/2 pot here. If he thinks he's trapping you then he'll raise you and you can consider a re pop AI or another raise. Likely he isn't and can get away from his high PP and might still call to see if you just have like QQ to 1010 (since board is low it's possible both of you have AA-1010 range in his mind).
Don't jam the flop or turn or river. No reason too. If he's even somewhat thinking he'll dump his high PP on flop or turn to that aggression, why risk at least $300 more to win $100 or so he will think. And on river he's going to bail if you bet pot or higher, he might bail on 1/2 pot but he might sigh call. Or even better might re raise you and then you GII.
As played good on flop and turn, on river bet 1/2 pot. If he calls good. If he re-raises you, fantastic and you can either 4bet it or jam all in (I'd 4bet if there's a lot still behind just to induce him rather than force a fold). If he folds oh well.