The Sony 20-70mm f/4 offers a broader focal range, beneficial for landscapes and street scenes, but is slightly heavier at 488g. The 24-50mm f/2.8 G is lighter at 440g, with a faster aperture for low-light situations, though it sacrifices some focal length. Both lenses deliver high image quality; the choice depends on your priority between range and portability. 

I love Sigma 24-70 f/2.8 DG DN II, but it is a bit heavy.

If youre analyzing the market for the best balance of weight and performance on the a7CII, you really gotta look at the Sigma 28-70mm f/2.8 DG DN Contemporary. Honestly its the lightest f2.8 zoom on the market at about 470g and it basically feels like it was designed specifically for these smaller C series bodies. From a technical standpoint, you lose that 24mm wide end, but the weight savings are massive compared to the heavier Art series or traditional 24-70mm glass. Another high-tier option for travel is the Tamron 28-75mm f/2.8 Di III VXD G2. Tbh this lens is a total workhorse and the VXD linear motor provides incredibly fast autofocus that keeps up with the AI tracking on the a7CII perfectly. If youre doing street or everyday scenes, having that constant f2.8 aperture is gonna be a lifesaver when the sun starts going down. The industry trend right now is shifting toward these 28mm starting points because they allow for smaller filter threads and less glass which makes the setup way less front-heavy. If you want the most bang for your buck without breaking your back, these are the two I would be looking at for a travel kit.