4xbb raise would generally indicate AK AQ PP AA-1010's

depending on the style of your opponent, i believe with JJ, a fairly strong hand it could have been effective if you took the lead in this hand...i.e. reraise on the flop to see if he has an over pair or if he flat calls than it may indicate small pp to AK AQ... with the flop he would check to you than a 3/4 pot size bet could let you know exactly where you stand... you also had position as well. this would be one possibility the hand could have been played.