Something that 'sits well' with you is easy to accept or agree with. When you say something doesn't 'sit well' with you, it means it makes you uncomfortable or uneasy or causes you to question or disagree with it.

1. I was thinking that we could finish up here and then go out somewhere for dinner. How does that sit with you? 
2. Darren's explanation of how the accident happened doesn't sit well with me.
3. The council's decision to reject the proposal did not sit well with the rest of the committee.

1. Alex had never been accused of being incompetent before, and the remark did not sit well with him at all.
2. Some aspects of the deal didn't sit well with them, but I promised that we would iron out any wrinkles before putting pen to paper.