Answer
Salam Dear Aisha,
Thank you for your question and for contacting Ask About Islam.
To begin with, we need to differentiate between heaven, the sky, and heaven, the Paradise. There is definitely mention of seven heavens (i.e. skies) in both Quran and hadith. However, the only hadith talking about this subject is weak so we may not rely on it totally.
Also we must mention here that the Prophet’s companions and early commentators of Quran accepted this statement as is, and did not mention anything about it; so we have to make some assumptions depending on scientific information that we currently have, which they didn’t have in the past.
With the above information at hand, some of the Quranic verses seem to imply the earthly heavens while most verses and the only hadith are definitely talking about much more than our earthly heavens.
I will list next the Quranic verses and briefly classify, again using logic, those that seem to imply earthly heavens and those that are not. To be clear, the seven earthly heavens are the ones starting with the troposphere and ending with the exosphere. The seven heavens beyond our earth are the ones theoretically belonging to the seven super-universes one for each super-universe.
Keep in mind that this will be my own judgment and anyone may refute it since this subject, even scientifically, is still open for debate; especially the assumption of how many universes or super-universes are there. However, you will read online millions or even infinite universes but only a mention of seven super-universes. For our purpose I will use super-universes since this seems to reflect well with our subject matter.
{He it is Who created for you all that is on earth. Then He rose over (Istawa) towards the heaven and made them seven heavens and He is the All-Knower of everything} (Al-Baqarah, 2:29)
The mention of earth at the beginning of the verse would immediately seem that Allah is talking about the earthly heavens but the mention of the Istiwa (rising) could mean much more than that since Allah rises over His thrown (yastawi alal arsh) which is above everything that exists.
{The seven heavens and the earth and all that is therein, glorify Him and there is not a thing but glorifies His Praise. But you understand not their glorification. Truly, He is Ever Forbearing, Oft-Forgiving.} (Al-Israa, 17:44)
Again here the beginning seem to imply the earthly heavens but the mention that everything glorifies Allah is telling us the whole of creation; therefore inclusive of the universes and super-universes.
{And indeed We have created above you seven heavens (one over the other), and We are never unaware of the creation.} (Al-Mumenoon, 23:17)
This is again could be both the earthly heavens and the super-universes since they are both above us.
{Say: “Who is (the) Lord of the seven heavens, and (the) Lord of the Great Throne?”} (Al-Mumenoon, 23:86)
Allah’s great throne extends over the heavens (universes) and earth, and is above the highest level in Paradise. And Allah is their Lord, the Lord of the Worlds (Rabul-Alamin). Ubadah ibn Assamit narrated that the Prophet (peace be upon him) said:
“There are hundred levels in Paradise, between each level is like the distance between heavens (sky) and earth, al-Firdous is the top most level and from it the four rivers of Paradise flow. From above that is Allah’s thrown, so if you ask Allah, ask Him for al-Firdous.” (Al-Albani classified it as authentic [sahih])
{Then He completed and finished from their creation (as) seven heavens in two Days and He made in each heaven its affair. And We adorned the nearest (lowest) heaven with lamps (stars) to be an adornment as well as to guard (from the devils by using them as missiles against the devils). Such is the Decree of Him the All-Mighty, the All-Knower.} (Fussilat, 21:12)
This is clearly talking about the seven heavens of the universes.
{It is Allah Who has created seven heavens and of the earth the like thereof (i.e. seven). His Command descends between them (heavens and earth), that you may know that Allah has power over all things, and that Allah surrounds all things in (His) Knowledge.} (At-Talaq, 65:12)
Here there is mention of seven earths. If we interpret the even heavens to be our earthly heavens then the seven earths are the seven layers of the earth’s crust. Otherwise, we have to believe that there are seven earths similar to ours, one in each universe.
{Who has created the seven heavens one above another; you can see no fault in the creation of the Most Gracious. Then look again: “Can you see any rifts?”} (Al-Mulk, 67:3)
{See you not how Allah has created the seven heavens one above another?} (Nooh, 71:15)
{And We have built above you seven strong (heavens)} (Annabaa, 78:12)
The above three verses are clearly talking about the seven heavens of the super-universes.
Narrated Al-Abbas ibn Abdul Muttalib:
I was sitting in al-Batha with a company among whom the Messenger of Allah (peace be upon him) was sitting, when a cloud passed above them.
The Messenger of Allah (peace be upon him) looked at it and said: What do you call this? They said: Sahab. He said: And muzn? They said: And muzn. He said: Andanan? They said: And anan. Abu Dawud said: I am not quite confident about the word anan. He asked: Do you know the distance between Heaven and Earth? They replied: We do not know. He then said: The distance between them is seventy-one, seventy-two, or seventy-three years (the narrator was not sure). The heaven which is above it is at a similar distance (going on till he counted seven heavens). Above the seventh heaven there is a sea, the distance between whose surface and bottom is like that between one heaven and the next. Above that there are eight mountain goats the distance between whose hoofs and haunches is like the distance between one heaven and the next. Then Allah, the Blessed and the Exalted, is above that. (Abu Dawud; but classified as weak according to many hadith scholars)
The above hadith seems also to imply the seven heavens of the super-universes. Since it a weak hadith, there is no need to analyze it any further. In Islam, we may only rely on a weak hadith if it doesn’t deal with what is lawful or unlawful, and if doesn’t have anything contradicting other hadiths or have some strange statements. Here we have no way of telling, we just hope that the narrator heard and remembered the same words that the Prophet (peace be upon him) uttered.
We may easily conclude that Islamic sources are talking about seven heavens beyond our earthly skies.
I hope this helps answer your question.
Salam and please keep in touch.