曇る and 曇り: a cloudy sky and fogged glasses
Distinguish 曇る as a change from 曇り as a state or object. Read the sky and glasses separately, preserving tomorrow's cloudy forecast and the past act of wiping fog from glasses.
A change in the sky or on glasses
曇る（くもる） describes becoming cloudy or fogging up. 「午後から空が曇って、冷たい風が吹き始めた。」（The sky became cloudy in the afternoon, and a cold wind began to blow.） 空 is the subject of 曇って. The following predicate adds a cold wind beginning to blow.
「温かい汁を飲むと眼鏡が曇った。」（The warm soup made my glasses fog up.） In 眼鏡が曇った, the change concerns glasses and is past. Changing the subject from sky to glasses selects the fogging sense; translating it as cloudy weather would change the account.
A forecast and fog being wiped away
曇り（くもり） functions as a noun for a state. 「明日の天気は一日中曇りの予報だ。」（Tomorrow is forecast to remain cloudy all day.） 一日中 gives the duration of the forecast cloudiness. 予報だ identifies a forecast for tomorrow, not a report of conditions already observed.
「眼鏡の曇りを布で丁寧に拭き取った。」（I carefully wiped the fog from my glasses.） 眼鏡の曇り names the fog wiped away with a cloth. Unlike the verb 曇った describing the change, this noun is the object of 拭き取った.
Following the grammatical connections
In 眼鏡が曇った, glasses are the subject and 曇った describes their change. In 眼鏡の曇りを拭き取った, the fog on the glasses is what was wiped away. が, の, and を help identify the verb and noun roles.
The cloudy sky, tomorrow's forecast, glasses fogging up, and wiping that fog away each supply different information. No rainfall after the cloudiness is stated, so the weather example does not add rain as a result.
What roles do 曇る and 曇り have in 「温かい汁を飲むと眼鏡が曇った。」 and 「眼鏡の曇りを布で丁寧に拭き取った。」?
Show the answer and why
曇った is the verb form describing glasses fogging up. 曇り is the noun naming the fog wiped away with a cloth. These two sentences concern glasses and their fogging, rather than cloudy weather.