Classic trope is to carry someone who has a sprained/twisted ankle or a sore foot. I've done it 'cause I'm a sturdy little twerp. Actually carried other kids who got hurt on boy scout outings more often than same-age girls. (Carrying your girlfriend's toddler little sister on your back or shoulders doesn't count.)
The one time it would have been a big deal, when a female college friend got frostbitten toes, I got the job of running several miles in the snow to get help. Other guys on the trip were bigger and two of them got the carrying job.
That's an adorable Nagatoroface, gochisou-sama deshita...
Though I have to say, if Senpai can carry a girl just one year younger than him, plus her luggage, plus his own, even for a short stretch, he's actually pretty damn tough.
Although it may have been inadvertently, Senpai played the game pretty cleverly. He got to outsmart Nagatoro, then assuage her desire by losing the next one, THEN playing along with her obvious third game tactics & got a lucky feel of those delectable thighs for his efforts. I'd call that a solid win in the relationship game.