John Gill Commentary 1 Kings 2:20

"Then she said, I ask one small petition of thee; deny me not. And the king said unto her, Ask on, my mother; for I will not deny thee." — 1 Kings 2:20 (ASV)

Then she said, I desire one small petition of you
It was but one, and a little one, and therefore she hoped it would be granted:

[I pray you], say me not nay ;
do not refuse it, or deny it me, or turn away the you with shame and disappointment:

and the king said, ask on, my mother, for I will not say you nay ;
since it is a small one, as you say, and provided it is fit and lawful to be granted.