I like the check on the flop, if you happen to be beat you may save money, otherwise you give everyone a chance to catch up. Then I think you have to check/call the turn and pray someone makes a hand.
River I'm betting more, may even try to over bet the pot and hope someone thinks you're making a play.
Overall tho you played it fine, tough to make money with a junk board like this.
'Please, buy in with the full $10 so you can take advantage of big hands.'
Amen.