When you start poking into the source of a word, you never know where it will take you.
I am not exactly sure how the word "haw" came to mind, but it did. I knew it was the nictitating membrane in a cat's eye (so named for an ocular discharge--yuck--and of unknown origin), and of course it can be used to express laughter in print (see above), but that doesn't shine any light on the word which subsequently comes to mind, "hawthorn". Now, to look at it you'd think that it was decomposable into the word "haw" and "thorn", on the assumption that a hawthorn bush is or might be thorny, but such assumptions are not always correct.
In this case, though, they are. "Haw" is an Old English word for "hedge" or "enclosure", and the plant itself is thorny, all right. "Haw" in this sense comes from an ancient Germanic word, "khag", which shows up in a couple of interesting places: because it means "enclosure", it is ultimately the source of The Hague, a city in Holland (which they call Den Haag), and it also wormed its way into English as "hedge", which is delightful.
There are lots of Germans up where my mother lives: in fact, she married one. One of her close friends, who also married someone of Germanic stock, has the surname Hagedorn, which is the German word for hawthorn! And if you look at "khag" and then "Hagedorn" and "hawthorn", you can see the interconnections! Well, maybe you're not as excited as I was to learn that, but I still think it's neat.
And speaking of surnames: Nathaniel Hawthorne wrote a story called "Rappaccini's Daughter", the introduction to which refers to a French author named M. de l'Aubepine, author of such works as "Contes deux fois racontées" and "Le Voyage Celeste a Chemin de Fer." Aubepine, as you might perhaps have guessed, is the French name for hawthorn (from Latin "alba spina", "white thorn"), and the works cited are French translations of Hawthorne's own works ("Twice-Told Tales" and "The Celestial Railroad").