You may save some weight by going to a freewheel or cassette, but make sure you carefully count all the components you are adding.
Hub, freewheel/cassette, rear derailleur, hanger, probably a different chainring, whatever rear brake you choose, shifter, etc.
Unless you are going full racing equipment, you're likely going to have a couple of pounds of new parts. As mentioned, you'll likely lose the chain guard/chaincase (or go to a very short chainguard) which will save a bit. But, you could make that change anyway.
If you really want to save some weight and improve the ride, try
Compass Tires (now Rene Herse)
I don't see what type of tire you have. But, for example, 26″ x 2.3″ Rat Trap Pass Tire, Extralight is 418g each.
26″ x 1.8″ Naches Pass Tire Extralight is 300g.
You may also look at lightweight tubes.
If you are using a tire liner, try the Panaracer Flataway tire liner.