I'd like a lightweight, minimalist single speed with 26" x 1.75-2.25" wheels/tires and a relaxed riding position, but still essentially road geo (not a mountain bike).
And afordable (under 800$)
Basically a straight-up attack the road (and a lil off-road) bike for shorter distance, fun rides.
Does such a bike concept even exist?

The concept definitely exists, you just described it

I'd be looking among the CX bikes, your brief is basically what they are. Why 26"? If it's because you're small, fair enough, if it's because you're taking ideas from mtbs, don't be scared to go to 700c. The CX crowd run both geared and SS so you should be able to get something without having to remove the gears.

sounds like a single speed mtb...

Old French boom bike with tubular cross tires. Easily under $300.

https://purefixcycles.com/collections...ucts/the-bogey

https://purefixcycles.com/collections...ucts/the-chief

But what if he doesn't want a frame with a hamster tail, Scrod?

Though I think Scrod onto something with looking at FGFS related bikes since they match up well to what you want.

I was just using the Pure Fix bikes as an example.

If the bmx-style FGFS aesthetic isn't wanted, it wouldn't be too hard to set it up to look more like a road bike.

Thanks- I'll look into it.

Thanks. Except these bikes are 33 lbs!
I think the FGFS realm is the right place for me to be looking- the Redline Urbis is one of the only promising bikes I've found. But I can't seem to find a weight on it, and I'm afraid it's likely heavy. Most of the bikes in the FGFS seem to be built (unnecessarily for me) like a tank. I don't plan to be tricking on it.

Thanks. The 26" is just a personal preference. I currently own a 700c and it's okay, but just never felt right for me. I'm not a distance rider and I don't focus on straght ahead, smooth riding.

Have no problem with the 'hamster tail' although I have no idea what the purpose is for it being there.?
The bikes you mentioned are spot-on for my wants with the exception of the heavy weight. Know of anything similar around 20 lbs?

edit* I see that most of Pure Fix's fixie line are in the range of 21-23 lbs... so that's a possibility. Thanks for the help. Any more suggestion?