Here's why:
* "Weather" is uncountable. You can't say "one weather" or "two weathers." We use "weather" as a general concept.
* We use "what" with singular countable nouns. For example, "What a beautiful day!" or "What a tasty cake!"
Here are some ways to correct the sentence:
* "What terrible weather we have today!" (This uses the correct structure with the uncountable noun "weather" and emphasizes the general bad weather.)
* "It's terrible weather today." (This is a more straightforward way of saying the same thing.)
* "What a terrible day for weather!" (This uses a countable noun "day" and makes the focus on the whole day being affected by the weather.)