I’m not native, but koto here has a kanji equivalent (事) and is generally used to denote abstract “things” rather than material or tangible things. 「くらい」here is used to give an approximation of the time that day, but こと here is likely just a word referring to the day that had good weather

Anyone with better japanese, please correct me, I’d love to know more.

I would translate のこと as ‘regarding’ or ‘about’. It shouldn’t really change the meaning but is just a slightly more indirect way of saying ‘the weather will be x’. Maybe you’ve also heard of あなたのことが好き(すき)です as a way to confess your feelings. The meaning should be the same as あなたが好きです but it might be perceived as more indirect and polite I guess.