depend

[Taka]

Whether they go fishing or not depends on the weather.

If 'depend(s) on' was replaced with '(is) influenced by' as:

Whether they go fishing or not is influenced by the weather.

how would it sound? If it sounds wrong, why?

[JohnParis]

Both sentences are fine. I have said and written both.

[emsr2d2]

Whether they go fishing or not depends on the weather.

If 'depend(s) on' was replaced with '(is) influenced by' as:

Whether they go fishing or not is influenced by the weather.

how would it sound? If it sounds wrong, why?

It sounds OK, but I would probably use "is determined by" rather than "influenced" if it is the weather which actually leads them to the final decision on whether to go fishing or not. "Influenced" suggests that it is just one factor in their decision.

[Taka]

So it sounds OK. Good. Just as I thought.

I found a lot of examples of 'whether...or not depends on the weather' through Google search but strangely there was none of ''whether...or not is influenced by the weather', so I asked the question.

Thank you both!

... if it is the weather which actually leads them to the final decision on whether to go fishing or not. "Influenced" suggests that it is just one factor in their decision.

I agree.