Here's some speculation from the Song Meanings site. Everyone's got an opinion about Madame George, it seems.
musiclover43 - "and you think you'll find a bag(heroin) the game wink out and your knees begin to sag" i also think that the word "Drag" has been around since long before 67, the English had been dressing like women in plays(Monty Python) just a thought.
stevecaratzas - I'm quite surprised to see that no one has mentioned that Van Morrison's actual name is GEORGE Ivan Morrison. Just sayin'.
And then your self control lets go
xhohxua - 'Madame' is one who runs a house of prostitution and George equals heroin, so the house is really run by heroin is the meaning and main character of the song. Ford & Fitzroy tendered piquant delicacies and objets d'art, along with delusions made real ... just so long as you could pronounce them with a mouthful! I know, I was there. It was a mighty long time ago -- mighty like a rose
Bocca - Of course the transvestite idea is rubbish. It was started way back by a really drugged out Rolling Stone writer named Bangs and Van has denied it. Bangs based his theory on the line playing dominoes in drag. I hear it as "and drag" that is inhale. It's about mystic transcendence that's why he called it Astral Weeks. George is definitely a composite character maybe partly his Aunt Joy and partly Mrs WB Yeats who went by 'George' and probably others. Clearly drugs were involved but it's not clear how. The only thing for certain is that it means something different to everyone who listens to it and that's one of the many reasons it's the best LP of the era. I was 16 when I first heard it in 1968 and I still listen to it religiously.
willard - It's actually about a transvestite drug dealer from Dublin who used to travel to Belfast to do business which is where Van came in contact with him when he himself was just a boy. Madame George's death obviously had an effect on Morrison - "Dry your eye for Madame George"
SPLINTER31 - The main theme of the song is about leaving the past behind. The character of Madame George is considered by many to be a drag queen, although Morrison himself denied this in a Rolling Stone interview. He later claimed that the character was based on six or seven different people: "It's like a movie, a sketch, or a short story. In fact, most of the songs on Astral Weeks are like short stories. In terms of what they mean, they're as baffling to me as to anyone else. I haven't got a clue what that song is about or who Madame George might have been."