low limit multi-way hand. Please berate me.

[MrDannimal]

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i agree with aargh57, betting out the flop doesn't protect your hand against any flush/ straight draw. Preflop action came from the CO, looks perfect for a CR to charge the draws 2 bets. After that, never fold a set and hope to fill up when on the river after the board gets ugly on the turn.
Q.

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This is silly. The pot is 16.5 SBs. If the CO bets out like you want, and either the button or BB calls, your raise is offering 20.5:2 or over 10:1. With implied odds, a gutshot is right to call there. Flush draws don't care about a raise, they're getting odds to call anyway. Anyone with a pair is getting odds to call and hit their 5 outer.

A checkraise isn't really any better at protecting the hand than betting out.

Here's the rub: You don't really need to protect your hand here. You have a set. Yes, there are straight/flush draws out there. But you're well ahead of them and have 7, then 10 out re-draws to a boat. Bet out and hope you get raised so you can 3-bet.