here is a better example let's say you attended a party were you had to wear Yellow or blue T-shirt.. the choice was up to you let's say 20% wore yellow & 80%blue. although 20% is a minority it is still sizeable as it's 1/5 of the people at the party. yellow T-shirt wearers are still a sizeable minority. strange party I know but just for example .

It means that although it is a minority it is a large minority. For example if 40% of all the cars are red, we could say that a sizeable minority are red. Whereas if only 5% of all the cars are read we couldn't say it was a sizeable minority.

sizeable means more then little minority means not the main type of person to avoid discrimination let's say aliens lived in England but they are minority as there are more humans but still there is a large amount of them (sizeable) a sizeable monitory would mean there are a lot of the minority "there is a sizeable minority of aliens in England"