I'm still curious how V1 = 116 & Vr = 137. That could have been a highly contaminated runway. 137Kts does not seem such a light a/c to a B737 pilot.
There are situations where you may/should/could reject after V1, but all of them sort of follow the Boeing song "unable or unsafe to fly"
B737. You are on a long runway; Vr is about halfway down, you attempt to rotate and nothing happens, the elevator is jammed. What do you do?
RTO?
Attempt to rotate on the trim?
Think WTF and depart off the end still pulling at high speed?
Just a little bar-room debate.