The body can make a substantial difference but if you're using big lenses on your DSLR, you're probably going to be using big lenses on your mirrorless too. The weight of the lens is down to the optics and build rather than the mount. For me, the weight of the lenses is by far the bigger problem.

To take your SEL35F18F as an example, the lens weighs 280g. The Nikon DSLR equivalent, "AF-S NIKKOR 35mm f/1.8G ED", weighs 300g.

To go to extremes, Sony's SEL600F40GM weighs 3kg and so does Canon's "EF 600mm f/4L IS III USM" (admittedly, Nikon's equivalent weighs 4kg).

I'm not saying this to prove you "wrong" or anything, a Sony A7RIV weighs 665g to a Nikon D850's 1kg or a Canon 1DX Mk3's 1.4kg but switching to Sony might just be the difference between a 5kg kit and a 4.7kg kit: it's still pretty heavy.

I'm just pointing this out because when I was starting out I heard a lot of people talking about how small and light mirrorless cameras were. I think at the time this idea was focused more on cameras like the Olympus OM-D series. Amateurs/enthusiasts (including myself, who owned an OM-D) often didn't realise that one of the major reasons an OM-D kit was much lighter than a DSLR kit was that it was optically less capable due to the differences in sensor size. A big part of the reason an 17mm f1.8 MFT lens is so small is that it isn't equivalent to a full-frame 35mm f1.8 the way many people thought it was. It's more accurately equivalent to a 35mm f3.5 which could be made similarly light for the larger sensor, if anybody wanted that (but few people want that).

Yeah, I read an article a while back that was complaining that the new mirrorless cameras were claiming to be saving space and weight by being smaller and allowing better lens designs closer to the sensor. But they weren't. In actual fact, the lenses were bigger in a way that more than makes up for the smaller lighter camera body.

What they didn't point out is that those bigger heavier lenses are bigger and heavier because they are more recent, and the camera sensors are so detailed that the cameras need fantastically sharp lenses, which means that they are bigger. Also, people's expectations of the quality of lenses has increased. So, they could make some small light lenses, but then someone would pixel peep and complain about how blurry they are, when in actual fact they would be just as sharp as the old DSLR lenses, but the cameras are more able to reveal their shortcomings.