While they weigh more than regular tires, they weigh less than the combined weight of regular tires + pump + patch kit, so it's a net win on weight.
For me, the biggest win is not about not worrying whether or not I get a flat, it's not having to pump the darn things up week in and week out before going out on my (admittedly city commuter) rides.
What's referred to as rotating mass on a bike (usually talking about wheels+tires) is noticeable. Maybe not as much on your city bike, but the thing that usually makes a bike feel heavy is the weight of the wheels, not the overall bike itself.
Best of luck with them.
When I tried airless tyres (a long time ago though) the ride felt very "dead" and I haven't bothered with them since.
Tubeless however - that's the best ride performance that I've tried and you very rarely get punctures that the sealant doesn't fix.
The actual weight of the tyres won't make a huge amount of difference (i.e. the rotational mass) as it only really affects accelerating which is much less common than simply maintaining your speed.
Larger moment of inertia, though, so not a complete win. I wonder how the trade off works--where is the breakeven point between trading tire mass for mass being carried in a fixed position on the frame?
the issue with airless tires though is bot weight, but rolling resistance and handling. Both are much worse. It is going to feel horrible.