In summary, I think Catherine passes a test in chapter 10, and from that point onwards Henry is sending out courtship signals, which she fails to recognise for what they are, and he goes on to pass an unintentional test in chapter 24.

When John Thorpe accosts Catherine during the dance, the main things Henry knows about her so far are that she's good looking, open mannered, and easily amused. He may also know (from Eleanor) that she's taken enough of a liking to him, that he's not just 'out of sight, out of mind'. What he has no way of knowing yet is whether she's discerning. So, I don't think he's exactly jealous: he ought to be undecided whether she's worth being jealous about. When she tolerates John Thorpe's interruption for as long as she does, it's not a good sign. Perhaps she's flighty, and easily amused by any old thing? The conversation comes to an important point here: "...and, besides, I do not want to talk to anybody.” “Now you have given me a security worth having; and I shall proceed with courage." But it's not just the banter that he proceeds with. I think that that's when he starts getting serious. (Of course, I'm obliged to think that, because his father's interference would detract from the romance if Henry had left it any later to decide!)

Here are some of the signs that he's either a-courting or, perish the thought, playing some deeply deceptive game.

From ch14:
"... Miss Morland is not used to your odd ways.”
“I shall be most happy to make her better acquainted with them.”

From ch16:
"... convinced me of your being superior in good nature yourself to all the rest of the world.”