The correct answer is: no article, a
The weather was rainy and we made a bet whether you would come.
In this sentence, the word “weather” is a common noun, which means it does not refer to a specific weather event. Common nouns are not preceded by articles unless they are modified by an adjective or a possessive. In this sentence, the word “weather” is not modified, so it does not take an article.
The word “bet” is also a common noun. It is not preceded by an article because it is not modified.
The sentence could be rewritten as:
The rainy weather made us wonder whether you would come.
Or:
We made a bet about whether you would come in the rainy weather.