No benefit to using thicker tubes for side rails?

I’ve seen a few folks on here posting that they’re using 1" DOM 0.120 tube on the side rails an 0.065 tube for the gantry to keep weight down.

There isn’t any load against the side rails though… The belts carry all of the load to the corners. If anything, shouldn’t we be using the 0.120 tube for the gantry if we want more stiffness, or just making everything to 0.065 to save money on tube?

I agree with you. The side rails do support the weight and can sag if they are very long without supports, but the two gantry rails are more important for stiffness. If it were me and I were reducing cost, I would lighten the side rails and not the gantry rails.

On my double-decker I used 3/4" EMT for the side rails and 1" welded 0.120 tube for the gantry and Z. (I was remixing a bunch of parts anyway so it was not an issue to mix sizes.)

I hadn’t thought about sag from weight. Hmm!

Did you have to do any custom parts to mix tube sizes on your build?

Yes, all the parts that accommodate two sizes must be custom. I don’t recommend it, I just mention it because it pertains to your question about side rails.

There’s a definite benefit to thicker tubes, just hold on to them whilst you’re cutting and you can feel the vibration in them. Reducing this and making the machine as stiff as you can as well is the way to go.
On my machine all the static tubes are now 1" solid bright steel which is cheap for me at A$17 a m. Immediately I could see and hear it cutting better after changing these, next is to do the moving tubes, which should be another level of improvement again.
My machine is fairly big and used to cut aluminium part like this for example which is 3mm thick and done in a single pass:

Do you think the benefit is from added mass to the machine or tube stiffness? Think it would also help similarly to fill the perimeter tubes with concrete or something?

The density of concrete is less than 3 whereas steel is 7.9, the volume in the tubes is not that big, so personally I don’t think it’d help much. I’ve see it done on machines using big square tubes where it apparently it did help, but the volume is so much bigger.
But I’ve not tried it myself so I don’t know for sure, for me it was not worth the mess etc. to try.