Does Kirkwall have no middle class?

This. Merchants and artisans. As to where they live.... who knows?

Though I've read that the irl Middle Ages is when the middle class as we know it began to evolve. Before that you were either noble/sponsored by a noble, piss-poor, or shunted off to the priesthood.

Lol, that's a perfect description of Darktown.

I'd say Varric was middle class, perhaps he's the first middle class man in Thedas.

the dwarven merchant guild had the connection and money to be considered high class. as some mentioned before during the area represented in dragon age (real world's medieval ages) there was no middle class, you are either noble or you are low class even if you are rich. hawke after the deep roads expedition had both. varric as well, he just choose to stay in the hanged man, cause he's not a noble by heart (well not "noble" in the social statue meaning anyway ), even if he's good at playing one.

Varric is so rich they made him the viscount after he sunk a ton of cash into rebuilding Kirkwall.

To be fair, the "Middle Class(tm)" as we understand it really didn't come about until the Industrial Revolution, where most societies suddenly had a large portion of the low-income populace now possessing equivalent free-time as the aristocracy, and a marginal disposable income which lead to the rise of the various entertainment industries. And not restricted by birth-caste, as it were! The madness! The SCANDAL!

Until then, you were stuck the class you were born into barring some miraculous luck or advantageous marriage/circumstances because the society and culture simply were not built to handle anyone other than the aristocracy having such extravagences as "free time." You were either high-class and had the spare income and time to throw fetes and balls or you were dirt-poor and had to spend every waking moment protecting yourself from starvation and taxes.