hows the weather there?

For me, they're both fine. The only difference I might consider is that my reply to "How's the weather?" would probably be shorter.

How's the weather?
It's good.

What's the weather like?
It's good. It's really sunny and hot but nice and cool at night.

How's the weather?
It's terrible.

What's the weather like?
Awful. It's been raining all day and they're talking about snow tomorrow.