Over the years my ever worsening physical abilities have made weight a primary concern for me and led me to try pretty much every format out there from compacts/premium compacts, bridge cameras, small csc's like the Nikon 1 series, micro 43, APS-C csc's, lighter DSLR's such as the canon xxxD series.
My findings are:
A - its always a trade off between smaller sensor size & iQ - The smaller the sensor size the lower the ISO where noise starts to become an issue, so whereas on the Fuji X-Pro1 I will happily shoot @ ISO 3200, on for instance the Olympus OM-D EM1 I restricted myself to ISO 1600 & on the Nikon P7800 compact to ISO 800.
B - Though body weight can be an issue its lens weight where the biggest problem lies especially if you want good fast glass with the average 70-200 f2.8 weighing in at well over a kilo as you know and longer lenses getting even heavier.
I found the Fuji lenses a little lighter than they're APS-C counterparts from other brands and certainly very sharp but the real weight saving comes with Micro 43 lenses, a 60mm macro f2.8 weighing under 200 grams, a 45mm f1.8 weighing the same, a 100-300 F5.6 at 560 grams and the superb Olympus 40 - 150 f2.8 at 765 grams so thats an 80-300 equivalent lens at half the weight of its nearest counter part.
Looking back over my wild life images the Canon 500D/Tamron 70-300 VC gave the best results, even when shot wide open & at higher ISO's but the raw's took a lot of processing to get really good images, next was the Fuji's with the added bonus that the jpgs where so good straight out of the camera I no longer HAD to shoot raw & process to get a good image.
I also had some great images from the EM1 micro 43 but I've just got the new body & lens so its to soon to comment really though I'm starting to feel that the combination of the pen F with its 20mp sensor & no AA filter and the 40-150 F2.8 could be the way to go for me with the faster glass meaning I can keep the shutter speeds up and still shoot at a low ISO, I guess time will tell.
The Nikon P7800 wasn't bad either with its fairly small size,long zoom range & fairly fast aperture ( f2.8 - f4 if memory serves me correctly) good controls, great rear screen but no view finder and it was that latter point that led me to change it more than anything else.
So its worth going to your local shop and trying a whole raft of different cameras, different form factors, different brands & styles and see what suits, but as already said don't dive in and get rid of the DSLR until you've spent some time with the new camera and are certain your making the right move.