LOL! Mythbusters did a show on this and proved she could have moved her fat butt and let him on. She must have been a democrat and saw herself as elitist and Jack as the lowly servant.
https://www.youtube.com/watch?v=JVgkvaDHmto&ab_channel=Discovery
IIRC, she tried to make room for Jack but when he tried to get on the piece rolled and threatened to dump her back into the freezing water. He chose to remain in the water to save her life.