Sensor size.
when i was doing research MFT wasn't giving neither cost or size advantage compared to APS-C
This can become true in some time when comparing APS-C and full frame.
Looking at camera bodies, yes. Most of the smaller-ish MFT bodies are in the same kind of size category as Fujifilm mid range cameras like the X-Tx0 and X-E series.
However, I would argue that the difference becomes a LOT bigger when looking at lenses.
There are some really compact and small lenses in MFT mount, lenses we simply have no equivalents of in Fuji X mount (like the 35-100 which is approx the size of a 35mm f/2 on Fuji, the 12-32 or 14-42 pancake zooms that are about teh same size as the 27 f/2.8. Also if you do a size normalized comparison, you generally get more in the same package on MFT : a 40-150 f/2.8 Pro Olympus lens is about the size of a Fuji 55-200, the Panasonic Lumix 35-100 f/2.8 is about the same size as the Fuji 18-55)
There's a lot of small pancake prime lenses as well : 14mm f/2.5, 17mm f/2.8, 20mm f/1.7, the two f/8 body cap lenses (9mm and 15mm)... whereas Fujifilm only has the 27mm f/2.8 and that's about it (even the 18mm f/2 is considerably larger and on the verge of not being considered a pancake lens anymore).
Even going outside of straight up "pancakes", you can get very compact lenses relative to their equivalent focal length, like the 12mm f/2, 17mm f/1.8, 45mm f/1.8, 42.5mm f/1.7, 75mm f/1.8 etc.
And on top of that, even if they're older bodies, you can get a substantilly smaller package by going with a small MFT body like an Olympus PEN E-PL or PM series, Lumix GF1 to 7, GM1 or GM5 or GX850/880.
I can understand the cost complaint... but even then, coming from a Fujifilm system this is pretty funny as Fujifilm lenses are notoriously expensive compared to most MFT equivalents, and the same goes for cameras (short of a few super-hyped products like the GM5)
I found that there was way less of a size differnece between my Nikon Z6 and Fuji X-T2 than there was between my X-T2 and Olympus E-M5 mark II.
I love (and use) all 3 cameras for different reasons.