After the suggestive comment from Vidar S. Ramdal, I decided to practically test whether different versions of the same file count towards total storage.
There can be three scenarios for this,
- Only the latest version counts towards storage.
- Total size of all the versions counts towards storage.
- Difference of various versions counts towards storage.
I created a site to test the above.
At the very beginning, there was no file in the site.

And the site usage was shown as,

We can assume that around 1MB is consumed as site overhead.
Then I uploaded a file of around 1 MB

Site usage was correctly reflected (1 MB + 1 MB = 2 MB) for version 1 of the file.

Then I changed a the file to bigger size, around 4 MB and uploaded this file.

Site usage was shown like this version 2 of the file.

File size increment, 3 MB. Reported usage increment around 3 MB.
Still, I uploaded version 3 of the same file.

Site usage was shown like this version 3 of the file.

File size increment, around 2 MB. Usage increment around 2 MB.
Finally, I uploaded a version 4 of the above file.

Site usage shown like this for version 4 of the file, with very slight change in file size.

File size increment, around 10 K. Reported usage increment was around 1 MB.
So, now this site have total four versions of the same file with the sizes 1 MB, 4 MB, 7 MB and 7 MB.
The total size of all the versions is 18 MB.
However, with the total reported usage being 8% of 100 MB = 8 MB.
So, we have very strong (circumstantial) evidence to suggest that Google uses an intelligent file difference policy to store the files. And hence only the incremental size counts towards total storage.
Finally, I replaced the file with a version of very small size.

The reported storage usage was like this.

This time, I am not sure what to conclude about storage usage. This is even smaller than the very first time.
However, we can safely answer to the original question that there is no need to worry about deleting old versions. We can leave them as they are without any worry.
Google is in a better position to comment on the whole issue.