Weight: system more important than sensor size?

You do not get the same exposure. Take a look at this comparison between the Olympus E-M5 and the Nikon D600:

http://www.dxomark.com/index.php/Cameras/Compare-Camera-Sensors/Compare-cameras-side-by-side/%28appareil1%29/834|0/%28brand%29/Nikon/%28appareil2%29/793|0/%28brand2%29/Olympus

Both cameras use recent Sony sensors, so it's reasonable to assume that they share technology. If you click on the SNR 18% link you'll see that for a given size print, the D600 has a 6 dB advantage over the E-M5 across the ISO range. 6 dB = 2 stops.

I don't need to proselytize about "equivalence" here, because everyone can plainly see that a 25mm F2.8 exposure from an E-M5 at ISO 200 is the same as a 50mm F5.6 exposure from a D600 at ISO 800. You get the same angle of view, depth of field, shutter speed and noise.