[gedanken]

This is messy bet sizes, but basically fine and normal. Lots of low stakes players love minbets for reasons that vary with the player a lot, and the situation a little. I like to keep notes on this, since for most players it means they have a weak hand and they're hoping you'll fold, but for some it means they have a monster they want you to bet for them.

I can't imagine the difference between .08 and .09, what? You can make it .10 because of the limper, or not, it's not that big a deal.

You're second raise is smallish, as mentioned, but I actually don't hate it. If you think villian could 3-bet from the BB as a bluff, almost any 4-bet will do the job. Once he reraises (even this silly .30), I think you can safely shove, because he's said he has a hand he'll play. $2.4 is a normal 3x raise, and good to get us pot committed.

Contrary to appearances, most LAGs are not looking for expensive confrontations with nothing. They're looking to take cheap shots at getting a big hand, then letting their image do the heavy lifting to get a call. He's got a hand here.

I'm glad you're not asking if you can fold your kings! Now that he's got the table playing back at him, JJ+ is enough for him to be going all in pre, probably worse.