My toilet won't flush when it's windy
It sounds like you have inadequate venting for your toilet.

In theory, all drains have a trap to prevent sewer gasses from entering your house. In order to drain properly, however, and prevent a trap from fully siphoning every time you drain the fixture (excluding how the toilet is special because I don't think it's relevant here), it needs ventilation.

This picture shows where vents are necessary.



The vent prevents the rushing water from pulling a vacuum and making it harder to flush or drain the fixture.

Now, you mention this is only a problem when it's windy out. Air moving over a pipe can create a lower static pressure in the pipe, and the vents often go out through the roof.

This may make it harder to flush since less air pressure is available to prevent the draining water from pulling the vacuum I mentioned before, so it will appear to back up slightly.

I haven't tried this before, but putting an angled piece of pipe on top of your roof vent may help solve the problem.

This is what I mean:



The red piece going over the existing vent could help prevent the wind from lowering the pressure in the pipe as much.