One of the reasons given for people having long peyos is because there is a prohibition to cut them very short and they are beautifying the mitzvah by letting then grow really long. My thinking that this is a reason is mainly hearsay. https://judaism.stackexchange.com/a/37316/12837 says something quite similar. I quote today's OU halacha yomi:
In addition, Rav Belsky, zt”l felt that extending the length of the peyos beyond what is halachically required is a fulfillment of the concept of hidur mitzvah, beautification of the mitzvah. Just as there is hidur mitzvah by using aesthetically pleasing objects (such as a beautiful pair of tefillin or a beautiful esrog – see Shabbos 133b) so too there is a hidur mitzvah by sporting longer peyos, which demonstrate our pride in the mitzvah. This is evident from the fact that Jews throughout the centuries, living in many different countries, have grown longer peyos than are halachically mandated. (Shulchan HaLevi p. 124)
I think the following question stands whether or not that which I have said till now is true, but this was how the question came to mind.
The source of hiddur mitzvah is shabbos 133b which a list of things that you can make beautiful. They all refer to mitzvos asei. Is there a source (as early as possible) for the idea of beautifying a la'av?
In case you ask, the logic for distinguishing between an asei and a la'av is compelling. You are commanded to do something so you do it nicely. If you are commanded not to do something, you just don't do it... you don't 'not do it beautifully.'