Well means "better"… Well that makes it easier to remember :)
Technically "Gwell" means better but it has mutated softly mutated so the "G" has been lost.
Same goes for "gwaeth" (worse), that's why you see "waeth".
Surely "The Weather Is Nicer Today" Is Right, As The Weather Being Better Would Mean It's More Nice, Thus Nicer.
In the context of weather:
Why is "weather's" not acceptable?
Duo sometimes gets confused about apostrophes and can end up suggesting, for example, 'weather has' when only 'weather is' can make sense.