I've had a couple of rifles that are conceptually similar to what the OP seems to be wanting -a Ruger M-77RL "Ultralight" in .250 Savage and a Savage Model 10 Sierra in .243.
I bought the Savage Model 10 Sierra in .243 used at a gun show about four years ago. This was obviously a short action mated to a slim-profile 20" barrel with the metal being blued carbon steel. The barrled action was fitted to a KEVLAR stock to make a blind-magazine rifle. At the time, I had no independent interest in a light .243 and only bought it because the $200.00 asking price was too low to pass up and I figured I could flip it later for a profit, which I did after keeping it a couple of years. At the time, it was the most accurate sporter-type bolt action rifle I had ever shot. It grouped .550" or less with boring regularity. It was my first and so far only Savage bolt action and mechanically, the only thing I didn't like about it was the bolt lift / cocking effort. I'm not a huge fan of synthetic stocks because I don't like the way they look, but if beauty to the OP is found in function over form, he'd do well to consider snagging one of these Model 10 Sierras.
Currently, I'm shooting a c.1985 Ruger M-77 RL "Ultralight" in .250 Savage. This is a short action with a slim profile, 20" barrel in polished blued carbon steel. The stock is checkered walnut, but much more slender than the standard M-77R stock of the same period. Advertised weight on these was 6.5 pounds. Mine is fitted with a period Leupold 33mm Obj. 2-7X Vari-X IIc in the factory Ruger steel ring mounts. It wears a simply nylon Mountain Sling carry strap. I seriously doubt if it weighs over seven pounds, field ready. It groups between .650"- .750" with factory 100gr. Remington fodder, and equally well with several different handloads including one that spits out 120 grain Sierra GameKings. It is a delight to carry. I don't even feel the thing on my shoulder when I'm carrying it on the strap, but I usually have the thing in my hands. It is the same length overall as my Marlin 336c, so it is a compact, handy size. Still, it isn't so light that it is insanely difficult to shoot from compromised field positions. These were also available in .243.
Between the two, I like the Ruger better. I prefer the aesthetics of its polished, blued steel and checkered walnut stock with its contrasting forend tip. The bolt lift / cocking effort of the Ruger is significantly less than that of the Savage. The Ruger also has a hinged aluminum floor plate, rather than the blind magazine the Savage had. It is probably a few ounces heavier, but it is still "feathery" to a guy who has mostly hunted with M-1903 Springfields and Ruger No.1-B's which aren't all that light. I also vastly prefer the .250 Savage because I think it has even milder report and recoil than the .243 but allows for a probably insignificant extra bit of lead to be slung with every shot -120 grain handloads v. 100 grain.
Apart from the fact that I like the Ruger M-77 RL enough to make it my main thing for the stuff I use a centerfire rifle for, it has sentimental value because I bought it for my dad way back when and it was his main deer rifle until he had to give up hunting for medical reasons. So, I'll never part with it.
But if I were looking for a replacement, I'd be leaning toward a Remington Model Seven CDL in .260 Remington. This is conceptually the same thing as my M-77RL -a lightish, compact bolt gun in a mild recoiling but sufficiently powerful and flat shooting round, with a traditional blued steel and walnut aesthetic.
I'm not sold on the idea that a rifle has to be stainless steel with a synthetic stock to withstand season after season of hunting use, and my 28 year old M-77RL kind of testifies to that, as it still shoots and presents as new, in spite of the use it has seen, which was pretty extensive for the first 12 years of its life. My old Marlin 336 that I've had since I was eleven still looks and performs great, too.
The Model Seven is available in different finishes / stocking if you have to have stainless and plastic. And you can it in .243 if you absolutely want to.
I mentioned my 336 and while it isn't a bolt gun, it is still a light, compact, rifle. With Hornady LeverEvolution rounds or equivalent reloads, it shoots flat enough and hits hard enough for any hunting I care to do. And mine groups those LE loads to 1.5" or less, so it is sufficiently precise. Mine has been converted to a "button style" half-magazine so it is a little lighter, a lot less prone to vertical stringing, and still gives me 1+3 firepower that I have yet to ever need in the field. I only mention this because a lever gun with a little gunsmithing can make for a nice, compact, fast-handling, relatively light, mild-recoiling but sufficiently powerful rifle, too... Especially in .30-30 when paired with the gummy-tip bullets...
The Ruger American has about zero appeal to me personally because I think its UGLY with a capital "U". But they are lightweight. They feel about as light to me as my M-77RL is. They are available in .243. The standard ones don't seem too compact to me, though.
There is the New Ultra Light Arms offerings to consider, too, though I wouldn't because still want polished blued steel and walnut.
Grist for the mill, as they say......
JP