The short stack OR is playing 46/32/20 over 800 hands, he is playing passive postflop though (low AF's)

The BB is playing 51/11/4 over 130 hands, he seems to be a very loose passive player.

I check behind here to under rep my hand a bit but also let other players catch up to flushes, straights or weaker full houses - I still think I can get a decent amount of value on later streets, especially in position and with my hand under repped. Do people think it is better to check or bet here? If bet then what sizing ?

After it being check round twice, I feel I need to bet start building a pot. There is some strange action after I bet; after the OR short stack jams I'm not sure whether to fold, call or raise now...on reflection I think calling is best to keep the BB blind in and the OR's range is pretty wide imo based on his style of play (~the BB might even raise with a weaker hand that would be dead if I am lucky)

Once the BB jams I have very good odds to call and the 2nd nuts...I didn't think he would have AA in his range that often (more likely K4 or 44, there is not a lot of kings left? lol) because of the preflop and his stats (which I've put above, he has a very high VPIP / Is a loose passive player), although I did consider that the OR could have AA - however I feel my range could be perceived as pretty wide as I only bet after beingchecked to twice.

Unfortunately I got my whole stack in with 0% equity, which is pretty depressing! Just a cooler or could have been avoided somewhere?