The gasket is not what seals it. It is what gets squashed when the lock points pull.
Follow the force. The handle turns a square spindle, the spindle drives the bolts along the opening edge, and each bolt is a mushroom head that enters a C-shaped keep on the frame. The mushroom's shape is the point: as it goes in, its sloping face rides against the keep and pulls the sash onto the frame. That pull is the seal. The gasket is a strip of rubber that gets compressed to about a third of its thickness by that pull — it has no power of its own.
Which means the diagnosis has an order. If the lock points do not bite, the gasket is not being compressed at all, and a new, thicker gasket will make the window harder to close while still not sealing — because it has made the interference worse without adding any pull. This is the commonest wasted purchase on a window, and it is wasted for a geometric reason.
And the bite is something you can feel with your hand, which is what makes this a five-second test rather than a job. Close the window slowly and pay attention to the last ten degrees. There should be a distinct change: the handle becomes harder, and at the end it seats with a small, firm stop. If it closes as easily at the end as at the start, the bolts are entering their keeps without touching them — the mushroom is passing through the middle of the C instead of riding up its slope. Nothing is being pulled, so nothing is being sealed.
Three faults, three tests
No bite, but everything moves is the lock points, and it is an adjustment. Each bolt sits on an eccentric cam: turn it and the bolt moves in or out by a millimetre or two. Slacken the small screw, turn the cam a quarter, close and feel. Work in quarter turns and test after each, because the useful range is small and overshooting means the window will not close at all. Once it bites, do the paper test at three heights — top, middle, bottom — and adjust the individual bolts until all three grip. That is what the separate cams are for.
The handle turns but nothing moves is the spindle: a 7×7 or 8×8 mm square steel bar that the handle grips at one end and the gearbox at the other. On aluminium windows it rounds off, so the handle spins on a bar that no longer turns. Take the handle off — usually two screws under a cover, or one grub screw — and look at the square: if its corners are rounded, replace the spindle, not the handle. If the spindle is fine but too short for the sash, the handle was replaced with one for a different profile and the bar barely reaches; a longer spindle is a two-pound part.
It catches at the bottom and the gap is wider at the top is the sash sitting low, and adjusting the lock points will only fight it. Look for a polished scrape along the bottom of the sash or the sill, and for a visible gap at the top corner. That is hinge wear or a dropped hinge, and the fix is at the hinges: most casement hinges have a height adjustment, or the sash can be lifted on its pins. Only after the sash is square again do the lock points make sense, because you cannot pull a parallelogram flat with a bolt.