Weight gain is one of the most popular transformations online and it is - by far - the most common transformation type in my stories. In fact, of the 28 stories I have there now, only two involve no weight gain whatsoever. When I first got into transformation fiction, I went to places that focused on this transformation exclusively, such as Mollycoddles and Dimensions Magazine. Mollycoddles has some of my older weight gain stories still posted, so if you really love them, by all means check out the stories of "Ghostly-Spectre" and tell me what you think.
Like most transformations, weight gain stories generally has three possible goals, which are not at all mutually exclusive. Punish/Humble people who deserve it, give someone a new role in life, or beautification. Generally the goal depends on if the author views curvy women (or men) in a positive or negative light.
To provide some examples, some see getting fat is a terrible fate that ought to befall bad people, and it ought to accompany other kinds of terrible changes, like in Mddubya's very, very dark story "When the cat's away." To others, weight gain might indeed be humbling, but it is part of a transformation from one role to another, like in Matt L's appropriately titled "Remodeled." And finally, some see the transformation in an exclusively positive light, such as Joel's "Life Changer."
The methods for causing the change are typically food, spells/wishes, aging, science, and even exercise, as in a story by Berry and one by me. Most readers, including myself, prefer a drawn out transformation process, rather than an instant change. Some prefer the end state to be quite large, others prefer only a smaller change. I'm on the small to mid-size change side myself.
The context of the transformation is that we live in a society in which being overweight is frowned upon. It is perceived to be a sign of ugliness, a health hazard, and by some even a moral failing. In some ways, this makes weigh gain seem more exciting - it is taboo. When I was younger, I dreamed of being the one guy who could see the beauty of an overweight person and heal their emotional wounds. This desire is reflected in my earlier works such as Embers in the Frost. I wrote "Embers in the Frost" as a teenager, and since then I have not tried to write a story where I describe my ideal women or my ideal relationship. I've changed a lot since then and I feel like I ought to give that a try when I don't have so many projects on my plate at once.
Some people look at weight gain as just a punishment, but others are overweight themselves or consider themselves to be FAs or "fat admirers." The Lard Biscuit site has a good explanation of what it means to be a FA today (it also has a gallery of plus size models.)