When courtie raises UTG this late in the tournament she reps something like:
{44+, A8s+, ATo+, QTs+, QJo+, K9s+, KJo+} along with some suited connectors every now and then.
She could lead the flop with pretty much any two hearts, a set for protection on a fairly wet board, a J or 2 pair, or a T with backdoor spades and potential other draws and of course overpairs. Our range now is:
{77, TT++, KQs, KJ/QJ/JT, Axs (hearts or spades) }. T7s or T8s and other smaller SC-type hands are unlikely here because of the UTG open.
After villain calls the half pot bet, courtie opts to check the turn. Villain can be calling with a heart draw, a T, or a J here. Thus, when courtie checks the turn, she has either improved dramatically or is attempting to pot control versus the occasional T in villain's range. However, if she had an overpair here like KK/AA, two pair, or top pair with a strong kicker, she would definitely bet to force a flush/straight draw to pay and/or get value off of a J. She knows that villain does not have many Ts in this position and therefore the check is either a strong hand or with intention of check-calling a bet w/ a draw, or just giving up on an Ax/missed backdoors and small draws to a big bet. She probably bets most of her higher J hands as well, although she may pot control this as she only really beats draws with KJ/QJ now.
{77, TT, JJ, KQ hearts, maybe KJ/QJ, Ax (hearts and A of spades)}
The turn changes essentially nothing for courtie, so after villain checks behind the turn, she knows he missed a lot of his draws. He would most likely bet a T on the turn so she knows he probably is not holding a Tx hand. She would assume that he bets a J for value so I do not think she puts villain on a strong J. She might put him on a pair like 88/99. He could also have slowplayed a monster but that is a but less likely. Thus, when she bets, she is either better a monster for value against a smaller hand, or trying to push villain off a mid pair type hand with a busted draw. She probably checks smaller jacks or pairs.
My best guess here is that she fires on Axs (hearts)/KQs (hearts) or 77/TT (with TT being way less likely obvs). Since someone already said KQ^, let's go with 77 (spade, heart?) (Also, I just do not think she checks turn that often with something like KQ of hearts, so many outs, so I feel she is usually much stronger or weaker here).