JJ vs R

[yocrackattack]

Been thinking a lot about this hand since, obviously, I lost it...sorry- didnt save HH but no big deal.

Sun Million with blinds at 1k-2k. I moved to the table 2 hands ago and have no info on players. I'm in cutoff w/ 45k and gun+3 w/ 35k makes it 3x to go. I just shove my JJ. I figured calling in pos was OK but a little on the passive side and repopping to around 15-18k would commit me anyway. I figured that by shoving I let him know he cant re-shove on me with decent broadways with any F-equity (though making it 18k commits me I cant assume donks know that). Of course I got called by AA and lost most of my stack. Who likes re-popping around 3x more and who likes calling here? If I just called what kind of flops am I gonna like playing shallow?