the EM5 is not much more portable then a 6D.
sure the 6D is bigger.. but in the end that doesn´t matter much (at least not for me) as the EM5 is not pockable either.
you need strap or a bag anyway.
No, the EM5 won't fit in most pockets, but to say it's not much more portable than a 6D (I'm assuming we're talking about bulk and weight here - obviously they're both portable in some sense) strikes me as bizarre. Not only is there a notable difference in camera body size, but you don't take photos with the body by itself - you need lenses. And the size and weight of M43 lenses compared to their DSLR equivalents are tiny across the board. There's simply no comparison between the size and weight of a body + handful of lenses between the two systems, especially if you like decent zooms and telephoto lenses. (My heaviest M43 lens is the Panasonic 100-300, but even that's just over a pound; imagine what a dslr equivalent would weigh and the space it would occupy!)
As for the rest, I hardly need to add to all the praise heaped on the EM5 in reviews etc. online, including from pros with FF gear: superb ergonomics, superb stabilization, extremely fast and accurate focusing (including focus points over the entire screen, not just lumped in the middle as with dslrs, plus there's no font/back focusing to worry about; my hunch is that with the EM5 there's a smaller focus fail rate than with any dslr, and for me that's very important), a surprisingly good sensor for its size, etc., plus a very good selection of often superlative lenses result in photos that are often hard to distinguish from those taken with a FF Canon + L lenses.
As it happens I have both a 6D and an EM5 and I plan to keep both. Given how good the EM5 is, why do I keep the 6D? First, I care a lot about background blur; and as a matter of course you get more blur at any given focal length and aperture setting with a bigger sensor (which isn't to say you can't really good blur with an EM5 - that's one reason why I like the Panasonic 100-300). Combine that with the fantastic bokeh of some some Canon lenses, and the results can be pretty irresistible (which isn't to say that M43 lenses don't have excellent bokeh). Second, I like taking photos in very low light; and while the EM5 is surprisingly good in low light (it helps that the in-body stabilization means that all their fast primes, unlike Canon's, are stabilized, which makes a big difference), no-one would deny that the 6D is better in this regard - its high ISO performance is pretty amazing. Third (and this is more subjective), I prefer the actual physical process of taking a photo with my 6D - I much prefer looking through a large, bright optical viewfinder even though, frankly, it gives a completely misleading impression of what the photo will actually look like (e.g. on the EM5 one of the dials adjusts exposure compensation, so while you look through the viewfinder all you have to do is turn the dial and, as you do so, you immediately see its effect on exposure). Fourth, the lowest ISO on the EM5 is 200, and if you peer closely at 100% on a good monitor you will see more noise/grain with the EM5 than with the 6D. Fifth, this may simply be habit, but I have a niggling feeling that FF photos, when everything goes right, are a bit better - but I'm far from certain that that's the case.
A couple of other DSLR advantages: they are probably quicker overall and thus better for taking photos of action (that's not something I do, so I can't really say for sure first hand). Plus, if you're into long telephoto primes, well, there aren't any for M43 - the longest right now is the (superlative) Olympus 75mm 1.8 (i.e. 150mm equivalent, which is pretty short by dslr standards). But of course if you're interested in minimizing the bulk of your camera gear you won't be interested in those anyway, even assuming that as a student you could afford them! (I have no idea how the two systems compare for flash usage - I've never used flash, including the cute little one that comes with it, on my EM5, and don't often use flash on my 6D.)
As for weather sealing, I have no idea which of the two bodies is more water etc resistant, but you should be aware that lens sealing matters here; and while I could be wrong about this I think the only two M43 lenses that are sealed are the Olympus 12-50 zoom and the Olympus 60mm macro (which is a marvelous little lens for other reasons too). But it should be easy enough to find out online.
I have no idea what your preferences/needs are, but given the significant differences in size and weight of the two systems, the differences in price (though some Olympus primes are more expensive than their Canon counterparts), and the small differences (if any) in photo quality much of the time, I wouldn't be terribly surprised if you went with the EM5.