Sticky is meant in a term that someone is very selfish, greedy, and/or petty.
They tend to bring up old favors that they've done for you or not want to do a favor for you because of petty things in the past
For example not letting you borrow something because of something that happened in the past or over something little.
Tim won't ever let me borrow something from him even though he borrows from me all the time, he's very sticky.