One of those songs which tells a nice little story and at the same time has an interesting message. It's about denial and social comformity. Billy Brown is a gay man who tries and hide the fact that he is by marrying a woman and having kids, the "perfect" model life. But then, like it always happens, the truth hunts him and he ends up being in a relationship with another man. At some point, everything bursts and he escapes. Once he escapes, he meets another girl and what happens? he begins once again the life that didn't work out in the beginning, the one with the wife and the nice house. And ironically enough, he falls in love with another man once again. Basically, it's meant to say that you can't really escape who you are. Life always makes sure you can't lie any longer.
I think the 'he met a girlie who was brave enough to say, " when they made love he shares the burden of his mind" is more like there was a girl who found out the two men got together and when that happened, billy brown was free of the burden of hiding his sexuality from others.