He was entangled by his own vanity, with as little excuse of love as possible, and without the smallest inconstancy of mind towards her cousin.So says the last chapter, with a couple of paragraphs about how he was led by vanity, curiosity and self-indulgence to first want to see Maria again, and to be determined to win her over when she behaves coldly to him-- it's humiliating, he's too used to every woman adoring him, and he thinks she's angry because of Fanny and tells himself he will overcome it. He initially intends a flirtation, but Maria's feelings for him are stronger than he realizes, and she refuses to let him go quietly. He never intends to abandon his pursuit of Fanny, and becomes quite frantic to keep the whole Bertram family from finding out what's going on between them, but Maria is indiscreet, and once the secret's out he feels there's nothing to do but go along with it.
So it's not that Henry ever decides to give Fanny up--not until he realizes all hope is lost anyway--but that he thinks he can flirt with Maria, make her his conquest again, mostly out of sheer spite, and then go back and resume courting Fanny. But Maria would rather be ruined that let that happen.