Um, that would need a dissertation, I think! One of the earliest incidences I know of is the myth of Heracles (Hercules) and Omphale, whereby - as the result of an oracle or prophecy - Heracles is sold as a slave to Omphale, Queen of Lydia. (We know it must be a dodgy deal because Hermes, god of thieves, con artists and used-chariot salesmen is the seller). In any event, the two quickly become lovers and one of their favourite games is to exchange clothes. Having cross-dressed for dinner one night, they retired to separate beds because they had to perform a ceremony that required chastity the next morning. Pan, who had been watching them earlier in the day, had the hots for Omphale, but didn't know about the clothes-swapping. So he sneaked into the tent and felt around the beds. Finding one with an occupant clad in silks, he crept in with 'her', only to be kicked across the tent by a startled Heracles!
If I had to guess, it comes down to this. When women were finally permitted on stage they could play ladies and ingenues and that was fine in straight drama or tragedy. Comedy, however, had different requirements. Cicero remarked that: "The key to comedy is to put a delicate idea indelicately or an indelicate idea delicately". Now in the 17th or 18th Century -when attitudes were more robust - this was OK, but come the 19th Century and Victorian ideas, it becomes less so. The idea of women speaking indelicately, or entertaining indelicate ideas however delicately put, was beyond the pale. But the customers at Music Halls still wanted the jokes. The answer was the 'female impersonator' - a stand-up comic dressed as a woman. There were stock characters, such as the Grand Lady, the gossipy older woman, the jolly-hockey-sticks tomboy or the working-class woman who was no better than she should be. They would mirror the male comics by talking about their husbands' or boyfriends' shortcomings, as well a criticising, in ribald terms, their female acquaintances. The acts were so popular that they continue to this day. However the decline of variety shows, both live and on TV, leaves most of them as 'club' entertainers with little chance of a breakthrough, while the rise of genuine women stand-ups has taken away the niche.
Many traditions of the British Music Hall made their way into the American Vaudeville and Burlesque traditions, and one of these was the female impersonator. The term 'drag' rose form the fact that long female dresses 'dragged' on the floor. So the connection between men in dresses and comedy is pretty much a fixed one in Western culture.
Please note that I am a Bear of Very Little Brain, so I'm not going to talk about any deep psychology here. It is also to be noted that most Black actors playing drag roles have done so only once, while numerous white performers have made a career of it! That said, many drag performers were or are gay, and there is still a lingering belief that Black men can't be gay, which, according to some, would make a Black man cross-dressing even funnier! This is certainly true when known 'straight' white actors take on cross-dressing roles, especially ones known for action roles.
