C/raising spot I need help with (10NL)

Villain is 32/22/3 and c-bets 100%


UTG ($5)
MP ($7.47)
CO ($10.45)
Button ($2.31)
SB ($12.01)
Hero (BB) ($10.20)

Preflop: Hero is BB with A, 10
2 folds, CO bets $0.30, 2 folds, Hero calls $0.20

Flop: ($0.65) 2, 10, 3 (2 players)
Hero checks, CO bets $0.35, Hero raises to $0.90, 1 fold

Total pot: $1.35 | Rake: $0.06

I've seen a lot of these types of players at 10nl. I guess they read somewhere about continuation betting and are doing it a 100% now.
His C-betting is obviously exploitable.
Same if we call a raise in position. He bets flop, we call/raise. If we call, a lot of times these guys check turn and we bet for easy win.

Now my questions about this:
Do we call with a wider range pre flop here against him?
How much wider?
How much does it matter if we hit or not? We're basically playing against his actions here.
Can we just call down when we hit, and raise when we miss?
I know I need to adjust to him, just don't know how much. I have the feeling we should put pressure on him almost always in these spots since it's so exploitable. See if he is adjusting and then take it to another level. Don't feel like I'm ready for that level though.
I don't even know if my thinking here is correct.

The way I do it now is to call a bit lighter, and to check raise/check call a bit more. I just don't know if a bit is good enough.