"Very tight" may be too tight on the winding spring!
The winding mechanism of a Leningrad is pretty simple: the winding spring exerts constant tension on the wind mechanism, which is restrained by a little catch until the shutter is released.
If you wind the spring too tightly, there may be too much friction to allow the catch to release.
More detail: This will be hard to explain unless you're looking at a Leningrad, but if you look up in the takeup chamber you'll see a shaft about where a normal camera would have its sprocket shaft, and at the top of it is a little flat spring-loaded lever that swings back and forth. This lever controls the action of the winding mechanism. On early Leningrads, the lever is loaded by a rather limp little hairspring; if the camera is wound too tight, this little spring won't have enough power to overcome the friction caused by the winding spring pulling against the catch. Later Leningrads have a much heavier hairspring on this little lever, and these seem to wind more reliably.
So, what you need to do is find out by experiment how much to wind the knob, and how much is too much. Tightening it until it feels really tight is likely to be MUCH too much! Try giving the knob about six turns; if it advances as it's supposed to, you can try a bit more until you exceed the limit. The amount of winding it will tolerate seems to vary considerably from one Leningrad to the next.
Incidentally, once you've found the proper number of turns for your camera, it may still hang up occasionally, and here's a trick that often will free it: turn the shutter speed dial (without lifting it) back against the spring tension about 1/4 turn, then release it and let it snap back under spring pressure. Often this will free the tension enough to let the film advance to the next frame.
