IPA: /ˈweɪt.ləs.li/
KK: /ˈweɪt.ləs.li/
In a manner that is free from the effects of gravity, as if having no weight.
The astronaut floated weightlessly in the space station.
Weightlessly → It is formed from "weight" (from Old English "wiht", meaning a quantity of heaviness) and the suffix "-less" (meaning without). The word "weightlessly" means in a manner that is without weight or heaviness.
Think of being 'without' ('-less') any 'heaviness' ('weight') — that's what weightlessly means.