thicker strings give u more headstock pull, cause more neck bend and may acually stop some types of buzz. this depends on the current neck angle, the nut cuts (like said) and the type of guitar.

Do heavier strings reduce fret buzz?

Yes – in some sense. Heavier strings have bigger tension, and therefore the amplitude of their vibration is lower. ... If you experience fret buzz when you put lighter guitar strings, it's probably because the action height is not properly adjusted.

Do Thicker guitar strings sound better?

Thicker strings will be louder than thinner strings without an amplifier because they have more mass, But that does not necessarily mean they sound better. Thinner strings make guitar soloing easier and are actually preferred by some of the heaviest sounding famous guitar players.