Here is some of the "evidence" that I have found:
Musonius Rufus, am ancient Stoic Philosopher, argued in Fragment 21 that men and women should not try to look androgynous by the way that they wear their hair, which supports Paul's discussion of hair length.
The ancient geographer Strabo, in Geography 10.3.8, and Epictetus, in Discourses 3.1.24-36, both argue that men and women could be identified by the way that they wore their hair, which again supports Paul's hair length argument.
Also supporting the hair length argument is a statement found in an ancient Hellenistic-Jewish document, "Long hair is not fit for boys, but for voluptuous women" (Sentences of Pseudo-Phocylides 210-212). By adding the qualifier "voluptuous," it appears the long hair had a sexual connotation as well.
The ancient Hellenistic Jew Philo also supports Paul's hair length argument by saying that men who make themselves look like women by how they wear their hair (amongst other things) are "worthy of death" and "debase nature" (Special Laws 3.37-38).
From David Garland's commentary on 1 Corinthians (pages 520-521): "For a Hebrew woman to go out uncovered was widely regarded as a disgrace (3 Macc. 4:6; b. Ned. 30b) because a covered head was a sign of modesty (b. Yoma 47b). To go out with loose hair in public (m. B. Qam. 8:6) was a greater disgrace and considered grounds for divorce (m. Ketub. 7:6; b. Ketub. 72a). Paul is not imposing Palestinian customs on the Corinthians, however, the Corinthian culture also looked askance at women going out in public without a head covering. The literature suggests that it was taken for granted that respectable women would wear some kind of head covering in public (...Plutarch, Mor. 232C, 267A). ... Uncovering the head in public had sexual implications. ... [quoting Thiselton] 'A woman who went out...unvieled forfeited the protection of Roman law against possible attacker who were entitled to plead extenuating circumstances.' ... Hair (exposed) is included in a list of sexual incitements in b. Ber. 24a." Garland then concludes his thoughts like this: "Women are not to be ogled as sex objects in worship. Paul's primary interest in this passage is to prevent this from happening..."
Charles Talbert, in Reading 1 Corinthians (page 87) writes that "In a pagan millieu, the sight of disheveled hair was connected with the worship of Oriental deities (Tibullus says a woman friend let her hair down twice daily in the worship of Isis [1.3.29-32]).
Thus, adding all of this together, Paul seems to be arguing, along with the cultural norms of his day, that men should look like men and women like women when leading in worship. Also, leaders in worship (especially women) should not make themselves appear to be disgraceful (sexually or otherwise) with regard to their hairstyle or head attire. Lastly, Christian worship should look different than pagan worship, particularly with regard to female hairstyle and head attire.
Regarding the braiding of a woman's hair, that is not found in the passage, though the NT does address it elsewhere. Probably what is in mind is the over-adornment of the hair, not a simple braid.