“went on asking.” The Hebrew is “said to Abraham,” but the word “said” is in the imperfect tense, which is important in this context; the verse could have been translated, “went on saying to Abraham,” but since Abimelech was asking questions, “asking” is a good translation here. This was not a short conversation. Abimelech was a righteous man, and Abraham’s fearful action put him and his kingdom in danger. He wanted to know what caused Abraham to act the way he did, and he was genuinely interested both for himself and his kingdom, if anything needed to be changed, and for Abraham, if he could help Abraham in any way. Abraham was a great man, but great men have faults. Godly people help others to grow in the Lord (cp. Heb. 10:24).

“see.” An idiomatic way of asking, “What was your reason” (NIV). The idiom has been freely translated into English in many different ways. “Whatever could have caused you” (CJB); “What did you have in mind” (NAB); “What prompted you” (NET); “What did you foresee” (E. Fox, The Schocken Bible).