Traveling on separate tickets is a very different matter. Others may know more than I, but I have no idea what Delta can and will do at JFK as far as your checked baggage is concerned. In addition, you should be aware that your reservation from London to Bucharest, and any later reservations on that ticket, are subject to cancellation if you do not check in on time for that flight. You would be protected in the event of delays if you were traveling on one ticket with connections, but that's not the case when traveling on separate tickets.