I tried to verify if 'make both ends meet' is British English before I made a google search and found the Indian English notion. Evidently the idiom with 'both' is less common, isn't it?
It's less common probably because you can't have one end meeting the other without the other meeting it. Making one end meet doesn't make sense.
'Both' is redundantly used like this in a few phrases, such as "Are they both the same?" Of course, A can't be the same as B unless B is the same as A, so if either of them is the same as the other, they are both the same. If they are not both the same, then neither of them is the same.