The correct option is C The weather being too hot, we cancelled our shopping plans.
The absolute construction is a grammatical construction where the
absolute (along with a participle) modifies an entire sentence.
A
nominative absolute is a free standing part of a sentence that describes
the main subject and verb of that sentence. It can be placed before or after the sentence, and is usually a non-finite clause that does not express the tense of the sentence.
In option B, the absolute construction is used; "the weather being too hot" is the construction that modifies the clause that follows. Hence option B is correct.
Option A does not use an absolute construction. It uses the subordinating conjunction, 'because'. Hence A is incorrect.
Option C is incorrect because the sentences are not combined.
Option D is incorrect because the answer lies in B.