Hi
I keep reasonably across camera developments and did quite a lot of research last year when buying my current Canon kit; that said I am no expert.
Minor weight savings can be achieved by the Sony A7 series (full frame) or A6XXX (eg A6500) (APSC). However these savings would be largely negated by the fact you would still need a bulky lens and to my knowledge the Sony 100-400 G lens is the longest Sony E mount lens available for these cameras. I am not sure of other manufacturers such as Sigma make long E mount lenses but laws of optics mean they would still be heavy. I used several Sony cameras over many years and for the most part liked them, but they were the SLR-style A mount (ie the old Minolta mount) not the E mount.
The major weight saving in terms of a bird-worthy (ie long telephoto) set up would be smaller lenses, and for this you will need a smaller sensor, as you know. I have read generally good things of the Olympus set up you have researched, particularly the Pro lens, but have never used them. There will definitely be a sensor noise issue in going from full frame to 4/3 as Glenn notes, but on the other hand a high quality f4 lens will pull a little of this back compare to, say, the Canon 100-400 at its longest length. In addition I understand the latest top of the line Olympus has excellent image stabilisation, which will also help limit ISO for static subjects. I think the top of the range Panasonics (which have a common lens mount with Olympus) have similar performance although Panasonic seems to be moving more into video.
I think the only other cameras in the picture, to my knowledge, are the so called '1 inch' sensor cameras which are super zooms (ie all in one). Both Sony and Panasonic make well regarded examples of these. Reviews generally suggest the Sony RX10 mark 4 leads the pack in this area and it sports a high quality 600mm equivalent zoom. The '1 inch' sensor are definitely a step down in terms of noise performance and dynamic range - that said, they are capable of surprisingly good results, and the relative fast zoom and excellent stabilisation also help. I have a first generation RX100 compact which uses the first Sony version of a 1 inch sensor, and I can say that is produces pretty good results up to about ISO 800. These super zoom cameras are very expensive for all in ones, but then so is a pro quality lens for any other kit.
I agree with Glenn's comments about electronic view finders. I have used some quite well regarded EVFs in Sony cameras, and the more I used them the less I liked them. The main problem for me was brightness - in bright sunlight I found them almost unusable as they were too dim compared to the surrounding light levels (and I wear glasses and it is impossible to cut out ambient light). I was constantly cupping my hand around the view finder to cut out light which is not practical with a long, heavy lens. Give me a decent, 100 per cent coverage pentaprism optical view finder any day. However others love them for their size and the fact that 'what you see is what you get' (up to a point) if the viewfinder is set to mimic the picture settings. They also don't suffer from mirror slap which in practical terms means (the potential for) a quieter or even silent shutter and faster frame rate. I understand Olympus has one of the best but I strongly recommend you try before you buy, and use the camera in a variety of real world situations (not just in the relatively dark show room).
Hope these comments help and are not too much 'teaching grandmother...'
Simon