Thinnest Affordable Watches?

It depends on what you call affordable, but the Citizen Stiletto (eco-drive) is only 4mm thick.

Beautiful dress watch

I don't know what you consider "affordable" but Nomos Glashutte has several model families which are thin (under 7mm). On the top of my head, Tangente, Ludwig, and Tetra, but probably have more models which are thin. All of these models are around 1500 USD, IIRC.

Man... you read my mind or mind control me :-) I've just searched for one but maybe little bigger

The Nomos Tangente (Ref. 101 at least) is 6.2mm thin. Depends on whether you call 1.400€ affordable or not.

If you aren't offended by fashion watches and quartz, the Mondaine Simply Elegant has quite a cool story. Only 6mm thick. Design licensed from the Federal Swiss Railway's station clocks. It's a Bauhaus design icon even if not haute horology.

I'm curious what you'd think of a Luch Single-hander, actually. The Single-Hander 3.0 line (which I'd definitely recommend over the original line) is 10.2mm thick. but about 3mm of that is the domed crystal, so that might be a potential candidate.

Check out some of the Junghans pieces. Approx 7mm mechanicals. When it's on the wrist you can hardly see it from profile. 

Affordability is relative, but I really do recommend Cartier Drive de Cartier.

https://www.hodinkee.com/articles/cartier-drive-de-cartier-extra-flat-stainless-steel-yellow-gold-hands-on#:~:text=The%20proportion%20Cartier%20is%20most,which%20is%20just%206.6mm.

Ever heard of the "lip t18" watch? Perfect for people with small wrist and maybe not the thinnest one, but oretty thin. French brand with a kind of nice history.

Citizen Stiletto.

Sea Gull Thin Business Dress Watch.

Roamer used to have a collection called Super-Slender, and thin they were indeed. However, it seems that they were discontinued. 

The Longines La Grande Classique is quite a cool extra-thin quartz dress watch, but around the 1K USD mark, its affordability is disputable, certainly that's more than I'd be willing to pay. But with it being among Longines's bestsellers, they can be found for less in the grey market or at ADs' seasonal sales.

As for the Swatch Skin, I have one of these, a plastic 34mm. Bought it when I was a teenager - like, 16 maybe. 

The strap's done, and it needs a new battery. However, this little plastic-fantastic thing was something I really enjoyed. I intend to revive it. For old times' sake and to enjoy it once more.

Before I became interested in watches, I sometimes wore a Movado Museum watch, which I really liked both for how thin it was (5.6mm)  and for the simple and elegant design. The only marking on the dial is a gold tone dot at the 12 o'clock position. I know it's not well regarded in the watch world, but from a design standpoint, I think it's a winner.

Zampieri is a micro brand that makes a pretty thin watch. 

If quartz are ok, you can get some affordable ones on Ali:

All are below $10, the first are actually from Soxy. All variants of the "Geneva" come with mesh, 7mm thick, prices vary between $2.81 and $3.49 for the different color options. The Kemanqi is 6.5mm thick, all colours come with leather strap at $3.56. The Jenises is from Belushi, model 8012, 6mm case thickness. Various colours, either with mesh ($7.01) or strap ($6.11).

I'd recommend Spaghetti Scammeti dress watches. No, seriously, in the US ashford.com is selling Swiza watches for dirt cheap that are high quality. The Swiza plana models come in 40 & 42 and are under 10mm thick.

Before Skagen was acquired by Fossil, many of their models were under 10mm. Don't know about now.

These are all quartz models. Sub-10mm automatics are hard to find.

Mechanical watches:

Seconding what @ermant said, you might want to look at watches with the Poljot/Luch 2209 movement or the Luch/Vimpel 1801 movement.  Many models are 8mm thick, but I suspect some models could be slimmer.

It's easy to find models that are under $100.  As a bonus, both movements are shock resistant.

This one seems the high-end of affordability ;)

Mido Baroncelli III - 6.95mm, automatic

https://www.jomashop.com/mido-watch-m0274071101000.html

I want one of those still. They look like old train clocks :)

Little bit left field but have you thought about the Casio 'Film Watch' - depending on the exact model in the range I've seen claims between 5-6mm thick..?

Plus it's a Casio! What's not to like.

Isn't quite 7mm but I have a new seiko quartz that is 8mm. Still really slim. 

At 7.5mm it might be a bit outside the range but the Botta Uno 24 is an interesting alternative to the norm. 

Vintage watches are a great choice for this topic, especially quartz ones (which will definitely come cheaper). My experience came with an inherited Tissot Seastar Quartz which doesn't hold much value or prestige except being very comfortable on the wrist (and got more compliments than more prestigious watches, which left me kinda disappointed)

Beat me  to it!

That's a ~90€ Poljot De Luxe.

The Movement itself is 3mm thick, the watch 8mm thick. But 4mm of that 8mm is the crystal.

Swatch Skin Classic range starts at £96 pounds, only 4.30 mm thick.