"two or three stones" sound huge. We are 20k vs 14k, iirc that does not justify a three stone handicap.

Our games feel relatively close, it's just evident that he is always ahead.

On a 19 x 19 board the ranks are traditionally determined by the handicap needed to give an even game. So a 14 kyu would give 20 - 14 = 6 stones to a 20 kyu. 20 kyu is a rank that often sees rapid improvement, as the basic ideas "click" just through play and experience. You might be stronger than that now.

Handicap stones give a greater advantage on smaller boards, but 19 x 19 is the standard size. I've not seen any specific guidance for smaller boards.