So at JFK, DL flies out of T4, whereas KE flies out of T1. I don't think they would have allowed me to check my bag in T4 just to have Delta process it unfortunately, so I dropped my overweight bag off at T1 and the transaction was charged by "Korean Air".

On the bright side, I nearly missed my flight returning to NY due to massive traffic to the airport. I believe the conventional cutoff time for bag drop is 1 hour before the flight takes off, but they allowed me to check my bag at T - 45 mins. Pretty sure it was way over 50 pounds, but the lady said don't worry about it, just pushed the bag through, and told me to run to the gate lol. I guess she didn't want me to miss my flight heh.