To remain determined, resolute, or steadfast in one's opinion, belief, or perspective; to refuse to be persuaded by someone else into believing or doing something one does not agree with. (A less common variant of "stick to one's guns." Both phrases allude to a soldier remaining and firing their gun(s) at an enemy, even when the situation might be dangerous or hopeless.) The prosecution is going to try to trip you up with your statement and your alibi, but so long as you stick by your guns, there's nothing to worry about. I really admire Jess for sticking by her guns during college and not submitting to the peer pressure of those around her to drink or do drugs.