Usually go for a check call down line here or go for turn and river value. 3 streets isn't going to be that profitable often enough.

Preflop: Standard

Flop: Pretty standard

Turn: Check-back - you are not gaining value from his AX since you chop with them - his KX are close to dead - you are not giving out a lot of equity - we just don't have a 3-street value hand - and by checking back turn we allow villain to e.g. bluff with his missed gutters OTR or do something stupid.

River: Yeah this is just ambitious - are you trying to fold him off a chop? That is just not happening - are you trying to get called by KX? That also seems really ambitious

Just check back turn and vbet river for about 50% vs his KX - or call if he leads river after checking back OTT.

I like beting T with your sizing 1/2 pot and check back R ,since he is a fish he's not folding any Ax so chances to win the split are almost 0 and he can have better hands.