This sentence starts with D. an absolute construction. If you are unsure, just use the system of elimination to get the correct answer. A is incorrect because "weather permitting" does not have a preposition - the only preposition in the sentence is AT, which is found near the end of the sentence. B is incorrect because this construction is not an adjective - it does not modify a noun or a pronoun directly. C is incorrect because past participle of the verb to permit would be having permitted, and here, the present participle form of the verb is used. Thus, the correct answer is D.