Road/cyclocross frame?

Velosprints said:

I have a cyclocross bike ... The cyclocross bike is heeeaaavy. It has disc brakes. I’d like to upgrade the frame to something quite a bit lighter..

That won't work well enough to matter. The weight difference between two otherwise comparable frames tends to be in the 200 g range. To get a bike that's overall noticeably lighter you need to use a majority of components that are lighter than average. Only time a separate component swap can make a noticeable weight difference is with suspension forks. Going from a low-end, steel steerer fork to a high-end can save nearly a kilo.

Velosprints said:

I also have a road bike. It’s as light as a feather. It has calipers. It’s components are very old and I’d like to upgrade to something newer. Hopefully Di2.

Instead of buying both a lighter cyclocross frame AND new components for my road bike, is there a frame set that could serve as both a cyclocross bike AND a road bike? It would have to have disc brake mounts, and enough clearance on the fork and seat stays for some cross tires without looking weird when regular road tires are installed. Does such a frame set exist?

Easiest way forward is to start with a CX bike. Fitting narrower tires is ALWAYS an option.
IMO, someone would need to look fairly close to spot that you're riding a repurposed bike. It's not like people along the road will point and laugh.

Oh, and don't worry about what other people think. As long as a bike is road-worthy, who cares what someone else rides?
Ride more, fret less.

Velosprints said:

Also, while I am searching for this frame set, is there a particular measurement on a spec sheet that would specify the size opening/clearance of the fork and seat stays?

Only thing I can think of is the tire width it's intended for. Should be described somewhere.

Many road bikes today can take 28mm tires. If you find one listed that can take 28mm + fenders, odds are good that it'll be able to take 32 mm (low-tread) CX tires.
Look for "adventure" or "randonneur" bikes. Rando bikes can be a bit different in geometry than CX bikes, so will not ride quite the same.

Or perhaps a "gravel" bike. Many of those are intended for wide 650B tires, which might offer a tighter fit vertically for a 700C skinny tire.

I agree that you should probably start with a 'cross bike, as the current crop of disc-brake framesets typically have plenty of clearance that will allow you to go both narrower and wider if you wish. That will give you one bike for road, 'cross and gravel riding. Don't worry about having more clearance than necessary for road tires, as really, who cares? It won't be the lightest or sharpest-handling road bike, but it will excel at 'cross and be very good for both road and gravel.