In the referred example " no more than " is a way of telling "simply, just, only" in an otherwise emphatic way to drive home the assertion or negation.
MORE is the comparative form of " much & many". So it carries its normal meaning in this respect. It also means greater quantity/degree being used as adjective or adverb:
* 10 is 2 more than 8
* He is more in sorrow than in anger.
The two examples are cited only to show that if you stick to the lexicon meaning of ###no more than, you'll land at this meaning of JUST as is said by King Lear's youngest daughter, ".....nor more, nor less", about her bond with her father suggesting only "just or equals to".