This is not as silly a question as it may seem. This is very specifically mentioned in the libretto (the Beaumont version of it, at any rate) and is one of several things that has gotten buried in several later productions of the ballet.

Because he is a good dancer ;)

Exactly! Not only is he a good dancer, but he is the only person she's met who loves to dance as much as she does.

I wish people who stage ballets would go back and read the original libretto; they'd get some lovely ideas I think usually stagers start with the one they're used to and fiddle with it to make it make sense OR look at lots of other productions for ideas and put them all together (that is, that's what the ones who think do )

The original libretto -- at least, as rendered by Beaumont -- makes so much sense and is so darned DANCEY. Either he left out a lot, or much has been added. I didn't find a reference to a weak heart. Giselle likes to dance, i.e., play, instead of working, and her mother tells her to stop dancing, that she's dancing too much and will come to a bad end. "Just one more dance, mother. Just one more," she says.

Many of the edges of Romantic ballet were buffed off and sentimentalized later in the century, and Giselle seems to have changed from a spirited, shallow young girl into St. Giselle somewhere along the line. It's not in the Beaumont I have now, but I remember reading somewhere that when Hilarion asks her, basically, "So what's he got that I haven't got?" (hinting, inexhaustible supply of rabbits, a good job, a better hut) she says, "He is beautiful and you are not."

If Albrecht has his epiphany in watching the terrible results of his flirtation, Giselle herself was redeemed, saved from Wilidom -- a whole tribe of girls who didn't listen to their mothers -- because she is struck by Albrecht's sincere sorrow and repentance. There's a bit of humanity (Christianity, in this world) left in her and that's what saves both of them.

Albrecht is young, good-looking (ok - a good dancer), a little mysterious (in small villages everyone knows everything about everyone else), and Mom isn't smitten - so a romance with Albrecht has a whiff of the forbidden - something that would be enticing to a young, romantically-inclined girl. I think that Albrecht's attraction is something akin to that of a rock star to a contemporary teenager.

The REASONS, IMO, that Giselle's mother doesn't approve of Albrecht are 1)he's a stranger and not enough is known about him; 2)he's encouraging Giselle to dance instead of following more serious persuits; 3)she wants Giselle to marry Hilarion. Hilarion is a forester and is, therefore, of a slightly higher social order than the rest of the peasants. He has access to the "fruits" of the forest - small game and wood - which are forbidden to the other peasants, and so is "wealthier". Giselle, by marrying him will never go hungry and will have a more comfortable life than she would if she married an ordinary peasant boy. Hilarion is also somewhat older, and so he can be expected to be steadier and behave in a more mature fashion than the rest of the "boys".