you definitely don't have to make it 4.5bb preflop when he has 39bb, unless you have a read that he folds to cbets a lot (many fish do).
I always look at their stack size and then strenght of my and my postflop plan when thinking about sizing pf unless there are people that will pick up on my smaller sizing with weaker hands.

Just shoving the turn is certainly an option, as no Ace or 9T 8T is folding anyway, but if you think he will call significantly more often with small ppsand 8x 9x when you don't ship it aight to bet like this, maybe even slightly smaller

larger flop bet (80c), shove turn (pot will be 2,65) he'll have 2,40 or something.

On that flop, there's like 16 combo's of TJ, 16 of 67, loads of Ax, some 97 n loads of stuff, ur ahead almost always, and on that kinda board, you get called, betsize not that important here, just make it so you can shove, the turn and river cards can just make him reluctant to call if he's weaker, + you want him to call with any 8 + draws on the turn when you shove and are ahead