First, I just had to share this article for your safety.

Second - what do you call your couch? When I was a child, we had a couch or a sofa (interchangeable words for us) and a davenport (the fancy one in the Living Room). I've never heard it called a three-seater . . . although I have heard "settee" before.

I don't think the article did call it a "three-seater". If you read it carefully from the beginning you'll see that it says in the sub-title, "A man who became trapped beneath his sofa for two days said he survived by sipping from a bottle of whisky." And then it continues' "...and fell against the three-seater which toppled onto him..."

The phrase "three-seater" was a descriptor for "sofa". It was a three-seater rather than a two-seater settee/sofa and I suspect that information was put in to make it clear that the item of furniture was especially heavy and that this was why the unfortunate 65 year-old Joe Galliott was obliged to remain confined, living off uisge beatha the "water of life".

Here we use settee and sofa about equally, couch hardly at all, and I agree with Richard that "three-seater" was an ellipsis for "three-seater settee/sofa".

Couch, then sofa here. Never davenport, seldom settee. Couch can be either two- or three-seater but haven't heard them referred to as such when offered a place to sit.
Once had a sofa-bed -- couch that expanded to allow for an uncomfortable night's attempt at sleep.

We always just called it a "divan." Wikipedia says "DaVan (d'van) was commonly used as slang for Davenport amongst the "blue collared" families of the 1950s/60s in areas of the Midwestern United States, especially Texas."

The Columbia Guide to Standard American English says "sofa, chesterfield, couch, davenport, day bed, settee, settle, studio bed, studio couch . . . are the names of long pieces of furniture designed to seat three or more adults; they are also suitable for one to lie on at full length. Some—the studio couch, for example—open into double beds. Sofa and couch are generic; the others are special kinds, except for davenport and chesterfield, which are also regional terms. All are Standard. See also CHESTERFIELD.

And I thought Chesterfield was a cigarette.