What is likely to be the weight difference between a 203/180 combo and a 180/160 combo.

Taking into account the rotors are Shimano XT so alloy spider.

Would I notice the weight difference in everyday use?

Not at all. 15-25g difference I would say. Better off going for a poo before you ride.

Or have smaller rotors AND go for a stool.

Bikeneil, thats probably why you’ll be quicker than me! 😆

I find that backing out a monster before a ride is most satisfactory.

if there is only a small weight advantage of smaller rotors why bother with them?

When I upgraded my brakes from avids to shimano XT, I found the 200mm rotor at the front gave me too much braking power. I like to have a bit of modulation rather than on/off that the larger rotor gave me. Dropping to 160 is perfect on the bouncer and run a 180 on the ridgid (29 er).

So to answer your question people select the size of the rotor primarily for braking performance. (torque = force x distance) the larger the diameter of the disc, the more braking force will be applied for a given lever effort.

I used to have 203/180mm discs, they rubbed more than smaller ones do, and I found the pads glazed easily, maybe not getting worked hard enough to get good and hot frequently enough?
Been on 180/160mm sets for years, now that my bikes more accurately reflect my riding rather than my aspirations 😉

Weight difference is in the region of 1g/mm

15 – 25g is a fart not a poo.