As others have hit on already, sensor size is the thing holding you back. Bigger image circles require more glass to resolve. The most compact FF e-mount option I'm aware of is Zony 35mm f2.8
Here's a quick size rundown. The zFc is very classic looking, so I included it. Had a n APS-C and is wearing a FF lens though. Next up is your A7c with the previously mentioned lens, followed by a fairly compact micro four thirds body and then the Nikon J5.
I'm a fellow FF Sony shooter and have found myself very fond of the 35mm focal length for a walk-around lens with my kids. My 35mm is Sigma's F1.4 DG HSM, which comes in at 775 grams and is fairly large at 77mm x 120mm. I've found myself grabbing my Sony FE 50mm f1.8 due to its much more compact size and weight, so I'm strongly considering a slower, but more compact 35mm to grab when I'll be outdoors.
I don't know if this is the case for you, but I am actively choosing my gear around gear I'll be more likely to use - even if this comes comes with some trade-offs in terms of IQ or aperture speed. My gear blows a cellphone out of the water for my hyperactive kids, but as they say the best camera in the world is the one you're carrying.