I have heard that the number seven when used in the Qur’ān refers to a large number. For instance where it talks of the seven heavens, we should interpret the verse as referring to “many” heavens. Could you please explain why this is so and on whose authority can we justify such an assumption?

This is not true. In the Arabic language, the number 70 is used in the sense you have referred to but the number 7 is not. For example, the Qur’ān says:

Whether you ask for their forgiveness or not [their sin is unforgivable]; If you ask seventy times for their forgiveness, Allah will not forgive them because they have rejected Allah and His messenger. (9:80)

Therefore, there are seven heavens (universes to be exact) in the literal sense as referred to by the Qur’ān at a number of places. (See for example: 2:29, 17:44, 23:17, 23:86, 65:12, 67:3, 78:12)