If you mean that you feel like you are losing subcutaneous body fat, but your scale weight is nearly constant, maybe you are slowly replacing fat weight with muscle weight? (And possibly denser bone, but I don’t know if that is really a thing.) You could check this by doing a series of body measurements with a tape measure every week or two (cloth dressmaker’s tape is more comfortable than a metal tape from the hardware store). If you measure the circumference of places that are basically skin and bone (like the wrist and ankle) or have only fairly thin, flat muscles (the waist), these may go down while more muscular areas (mid thigh, upper arm, calves) go up or stay nearly constant.
I have always been skinny and do keto for other reasons. My body weight had been 157 +/- 2 pounds from age 32 to 52. When I went low-carb, it dropped to 154 (which I’d rarely seen in that 20 years) and stayed there for part of a year. At the same time, I had to punch two new holes in my belt, so I interpreted this as losing some visceral fat.
After about a year weight slid back up to 157 and stabilized again. I do a fair bit of kayaking, and I noticed that my dry top (a size Medium that I had for over a dozen years, made of a material that should be able to neither shrink nor stretch) which had fit perfectly had become even harder to get off after paddling. I think that was because my latissimus dorsi (the main muscles used in kayaking) had gotten a little bigger, just enough to make it hard to pull the drytop off over them.
So, you may be getting recomposition without weight loss. Exercising, particularly weight training, would hopefully make that work even better. Even a couple of 45 minute gym trips a week can do quite a bit if you do a few “compound lifts,” meaning exercises that work more than one muscle at the same time, as opposed to “isolation lifts.”
(I like trap bar deadlifts, dips, pushups, bent-over dumbbell rows, banded clamshells, waist rotations with a cable pull and overhead dumbbell press. I do three or four sets of deadlifts then usually one or two sets of any three or four of the others per session, and while this is no great bodybuilding program, it does something. There are an almost infinite variety of other lifts you could do while hitting the same muscles, of course.)