@John_Doe_Jersey went and tested this. Not because of manga and all but just so I know that if there ever is a situation where person should be carried, that I can carry it or not.
So, can I? My girlfriend is few kgs ligher than I am (and few cm shorter, dunno how much height plays into princess carrying) and I'm at 76kg (and 186cm). Piggybacking is doable. Far from easy and even further than what usual manga shows but I could even run for some time. Princess carry is doable but running is out of option. Can walk around but it is way harder than piggybacking and way way harder than it looks.
My sister is at 50ish kg and 160ish cm tall. Can run even while princess carrying but I'd rather not. It's highly unstable and piggybacking is better option if running is required. And it's better for your back.
TLDL; I can princess carry myself but can't run with myself in arms.