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So about half the time you're 77-23 against overcards, half the time you're dominated against overpairs. You have also not gained any decent knowledge about what he holds that you couldn't assume when he called preflop.

Isn't it better to check the flop if he's calling with overcards?

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I bet from > 1/2 pot to pot on flop, fold to any significant aggression on turn, doubt he c/r's flop, but fold if he does.

If he calls with overcards, and lucks out, that's fine, we've his call is a mistake, he is calling with bad odds and will make us money long term.

Why would we give him a chance to catch an pair here for free, by checking the flop?

A lot of the time a player that passive will fold all but overpairs here to the flop bet, and if he calls the flop bet, we know not to put any more into the pot unless we improve.

That said, most of the time if he checks the turn and bets on the river (<1/2pot?) I probably call there.