PokerStars - $3.32+$0.18|10/20 NL (2 max) - Holdem - 2 players
Hand converted by PokerTracker 4

Hero (BB): 77.5 BB
SB: 72.5 BB (VPIP: 0.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 3)

SB posts SB 0.5 BB, Hero posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has 9 A

SB raises to 3 BB, Hero calls 2 BB

Flop: (6 BB, 2 players) 5 4 9
Hero checks, SB bets 3 BB, Hero raises to 9 BB, SB raises to 22 BB, Hero calls 13 BB

Turn: (50 BB, 2 players) 6
Hero checks, SB bets 22.5 BB, fold

SB wins 50 BB

Second hand of the match. Readless. Are we too deep to check-raise a TP that is likely to face over on future streets? Should I have folded to the flop 3bet? As played, fold turn?

I think check-raising here has no merit.
Against a reasonable $3.50 guy you are behind against any shoving range on the flop.
Plus I think that if he had some kind of draw in his hand like a good draw like 7d8d,6d8d,Ad3d,Ad4d,6d3d he would raise a lil more cause he would like to have good fold equity but I am really not sure about that i am making assumptions.
Lets analyze a bit more.
Lets say if the player is a decent guy who is not monkeying around or is on drugs he is doing this play with lets say this range in this particular board.

Hero:Ah9s
Villain:7d8d,3d2d,6d8d,Ad3d,Ad4d,6d3d,Ad9d,9d8d,TT-AA,AdTd+(maybe)
On the turn with this board you have about 36% equity and your pot odds is 3.1:1 or you need rougly23%eq to make the call.
So your call would be right BUT most of the times I wouldn't do it without reads.
If he do these mokey moves again well,you'll know to play your hands in the future against him!

Flat flop