Pour le Robert, l’origine latine est dans ce cas reddere et non rendere :

[§ C] Rendre : Verbe d’état suivi d’un attribut (du latin reddere « remettre en l’état antérieur », puis par extension « faire passer d’un état à un autre ») : Faire devenir.

I think you are talking of the 15th meaning on Wiktionary :

Faire devenir ; être cause qu’une personne, qu’une chose devient ce qu’elle n’était pas auparavant.

This meaning can be explained as something you are lending. When you lend money or goods, you are getting back the same or something more interesting. If you are “lending” your efforts, your time, your work force to create something, you are getting back (“on te rend”) what you invest in.

There is several meanings to the verb “rendre” in French. The origin you are referring to:

from red- “back” (see re-) + comb. form of dare “to give”

… corresponds to the meanings that have something to do with the idea of “giving back”/”restoration”. For example, the meanings that correspond directly to this origin in Wiktionnaire are:
1. Remettre une chose entre les mains de celui à qui elle appartient, de quelque manière qu’on l’ait eue.
2. Faire recouvrer certaines choses dont on était privé, qu’on avait perdues, comme la santé, les forces du corps, etc.
3. Faire rentrer (des personnes) en possession d’une chose dont elles étaient privées, ou à laquelle elles avaient renoncé.
… actually most of them.

But, you can observe that if you classify the list of meanings, some slip towards the meaning of “producing” or “giving the effect/meaning of”, for example:
8. (Économie) (Agriculture) Produire, rapporter.
9. Donner l’effet recherché.
10. Exprimer, représenter.
11. Traduire.

Note that the word “rendu” (nom masculin) stem from those meanings. And note that this group of meanings focus more on the idea of “result” than the previous group.

Actually, the verb “rendre” has been progressively enriched with the idea of “giving the characteristic” or “giving the essence” of something. This gives a creative dimension to the verb “rendre”. And it is actually pretty logical that a word that originally means “giving back” is chosen for the “characteristic” or the “essence” of someone or something.

Now you may better understand how “rendre belle” can mean “making this person/thing pretty”, or should I say “giving that person/thing the “pretty” attribute”.

15. Faire devenir ; être cause qu’une personne, qu’une chose devient ce qu’elle n’était pas auparavant.

The big evolution, here, is that “rendre” lost the idea of “origin” and “restoration”. “Rendre les clefs à Marie” -> the key are originally detained by Marie. “Rendre Marie célèbre” -> Although beeing famous is now part of Marie’s characteristic, the sentence implies that Marie wasn’t initially famous.

That is how the different meanings of “rendre” shifted from the idea of “restoration” to the idea of “result”.