It could very much so, I don't dispute that. I just tried to respond the best I could based on limited info from the OP. Having tried various systems I personally didn't find the A7 series gave me much a size and weight saving over a DSLR with comparable lenses. Obviously some folk feel different, and I guess when you use something like a 50mm f1.8 the overall weight saving with an A7 is circa 20%, which does sound significant. However, in the real world it didn't 'feel' that different to me. Maybe it's the grip or balance, which then becomes much more subjective and why there is a wide difference of opinion
But going back to the F4 lens for a second. If you look at the 24-70mm f4 on the A7II you could get the 12-40mm f2.8 on an EM1 which obviously has one stop better light gathering therefore narrowing the gap of the extra light gathering ability of the A7, plus the Olly setup is lighter and smaller even though it's f2.8 vs f4. Use the 12-40mm on the EM5-II and it's lighter and smaller still (camerasize has the weight wrong for the EM5-II).
There's just too much bloomin choice
And without knowing the OP's wants and needs we could go back and forth all day long