It seems to me "увлекаться" implies more involvement in the process. For example word "драка" - fray If someone "интересуется" - he stay in stands in the crowd of onlookers. Shows interest. If he "увлекается" - he is one of the fighters. Fascinated by the process and not see anyone nearby. But both imply participation in the process as an amateur. About Kostya Tszyu we should say "занимается", because it is the main thing in his life.

Интересоваться and увлекаться are mostly synonyms when we're talking about hobbies. Интересоваться is a bit weaker then увлекаться and means more like ask questions, do some research, etc Beside of this, it means just "ask question".

Below are the possible meanings of these two words with examples. интересоваться 1. be interested (in), to take an interest (in) интересоваться историей = to be interested in history 2. to ask, to inquire Он интересовался вашим здоровьем. — He inquired about / after your health. увлекаться 1. to take a great interest (in); to be keen (on) увлекаться теннисом [шахматами] = to be keen on tennis [chess] 2. to be carried away (by) Не гони так быстро машину, ты слишком увлёкся! = Don't drive so fast - you've been carried away! 3. to take a fancy (to); to be infatuated (by); to fall (for) Такой красавицей кто угодно увлечься может. = Anybody could fall for such a lovely. 4. be drawn (into) Дым увлёкся через дымоход наружу. = The smoke has been drawn into the chimney. HTH

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At first a person "интересуется " (чем-либо или кем-либо), after that " увлекается" or " не увлекается".