Size isn’t increasing with stretching. Example lets say you have a scene with a Skyhammer in it. The Skyhammer is taking up 50% of the scene height.
He will take up the same ammount of space wether you render to 720p or 1080p. Ofcourse a 720p image is smaller compared side by side to a 1080p image. But if you stretch them to the same space, Skyhammer will take up the same 50% screen space. Only thing that changes is that one image has less pixels to describe the scene (lower resolution) potentialy smudging fine details together, and by scaling up making everything either blockier or if the scaling routine does some kind of interpolating blurred.
Aside from this HUD elements could be unaffected because they are images themself and a dev can choose to not scale them up to always take up the same amount of screenspace (to prevent image interpolation blur), those would apear bigger when stretched.