I only just saw this post, but I've been on Linzess for about a year and a half, and it has had little to no effect on my weight or appetite. Diarrhea is common, especially at first, which may cause some temporary water weight loss, plus it's always nice to clear out any stool that has overstayed its welcome before weighing in.
It does still give me diarrhea sometimes, but my bowel habits are much more predictable, and more likely to happen multiple days in a row if I take it every day as prescribed. Only caveat is that if I'm restricting below like 900 calories for more than 2 days, I need to have plenty of fiber to add bulk to my stool. If there's not enough, then I still go a good 3-4 days without a BM despite taking Linzess.
I still experience abdominal cramping, too, but apparently a lot of the people who take it for IBS-C get less abdominal pain when they take it.
If you have any questions about some more specifics, feel free to ask!