I'm thinking maybe the whole stairs thing is supposed to be symbolic in a way. Like, Jun wants to continue being competitive against Tomo, always as a friend, yet now also as a romantic partner, because not only is it fun for them, but Jun strives to be on the same level as Tomo (or at least close enough to her level in order to 'deserve' her or to feel worthy of her), since he admires her so much for her strength, her speed, her stamina, and her fitness: so those are the qualities Jun wants to constantly be improving in himself. Then the relationship will be one of equals, as he sees it. With the added bonus of still being two friends who are active and playful together, etc.
Ah, but Tomo skipping two steps at a time -- always one step ahead of him -- I think it amuses Jun, and he can continue to admire her...which is all pretty cute. ?
(Assuming that's the sort of direction where this is headed.)
@Rozoro -- That's brilliant! ? I think you're absolutely right. What an interesting assessment.