Visualize what's happening.
Unfortunately the PHB doesn't give much of a visual description of what Blade Ward looks like...
I used to think that dozens of spectral daggers appear around you deflecting some blows.
In any case, being a ward it means that it's something outside of yourself, like a force field, which means that whatever weapon reaches your flesh, it first crosses this ward and then your heavy armor.
(Of course you could view this ward as a thin barrier over your skin, which would change the order of effects... but I wouldn't call that a ward)
With Stoneskin however, its resistance is the last one to be applied, because as the spell says it turns your skin into stone. Which is under your armor.
