Immersely means very much — not a little, and not only 'quite a lot', but to a huge degree. We almost always use it with feelings, thanks, and how strongly we like or dislike something: you can enjoy a meal immensely, be immensely proud, or find a film immensely boring. It does not usually describe the size of a thing sitting in front of you; that job belongs to the adjective immense. Though actually, people do stretch it a bit ('immensely popular', 'immensely helpful'), and nobody thinks of a giant object then — they think of degree. It is ordinary English, not slang and not stiff; teachers, books, and everyday speech all use it. If you only need a small word, 'so much' or 'a lot' will do; immensely just turns the volume up.