The camera body of a mirrorless camera is always going to have the ability to be smaller (it doesn't have a mirror box), there is no way "around" that. And on the camera forums out there, this has been a topic of hot debate for years and years. Plenty of articles/forum posts out there if you want to dig deeper into that.
But basically, lenses for any given sensor size, will always need to be fairly similar in size, because its the size of the image circle (and the aperture) that determines most of the lens size, not the size of the body it connects to.
That said, in some cases, the shorter potential mounting distance of the mirrorless
does allow for a different optical design technique, making for smaller lenses (wide angle lenses only AFAIK).
So if depending on how many lenses you carry, and what type they are, the total system weight/size may not be all that much different.
A flip side to the smaller physical size, is often times mirrorless cameras have less physical places for buttons, and are smaller/slipperier to hold, especially if wet. This is primarily an issue with larger lenses (large aperture telephoto lenses) that are weighty. Just because it gives the camera/lens setup an unbalanced weight distribution. Most smaller cameras are harder to use with gloves too (again, probably not an issue, but some people care a lot about that).
Anyway, just pointing out that while there are clear differences, its not quite as clear cut as "mirrorless is better". Like most things, its better at some things, and not as good at others.
If you're looking for smaller/lighter kit, the easiest way to do it is to shrink the sensor size. Because that shrinks the required size of lenses, and everything else.
I'd seriously consider the Panisonic GX85 (or similar micro 4:3 camera) if you're looking for a small ILC (Interchangeable Lens Camera).
https://www.amazon.com/PANASONIC-12...keywords=panasonic+gx85&qid=1582569274&sr=8-3
It is listed in DPReviews most recent "Best bargain cameras of 2020" list as well. You can find a link there to their full review if you're interested.
https://www.dpreview.com/reviews/buying-guide-best-camera-bargains#gx85
And here is a useful tool comparing sizes of cameras and lenses. You can see how much smaller the GX85 is than your 60D.
https://camerasize.com/compare/#100,673
Anyway, good luck with whatever you do

.