Yea, your pre-flop ranges are not reasonable. OP didn't specify but villain's stats are likely just averages, so his 3-betting range will likely be higher than 20%. But even if your range is correct, I wouldn't be confident you will have 42% Equity when he jams. Stations are more passive and you are lucky if you even have enough equity to call a jam let alone expect to have 42% equity. Villain calling more and raising less on the flop is favorable for c-betting, but villain will still likely jam often enough to make checking back a much better option.

Checking back may seem weak, but there isn't much you can do. His range connects with this board. Having to bet/fold or bet/call w/ our equity is a very poor result for us.