I think it varies - many can be average cat size, although you can get big males. My previous Abyssinian, Simba, had an average weight of around 6kg as an adult and he wasn't fat he was just big and muscley.
Modern abyssinians are not a wild breed, despite their looks. I think the origin of the breed is uncertain, but it's been around in Britain for over 100 years - one of the longest established breeds. To make an abyssinian these days you breed two abyssinians . I think how common they are varies from country to country - in Britain I don't think they're that common, there certainly aren't so many breeders as there are for some other breeds (e.g. siamese, bengal, etc).