No you are not weak! It is surprising when manoevering stairs, just how tricky it can be. I’ve had that problem with what you are describing, the lip on the edge of the stairs. I suppose that the wheel is just catching under the lip and making it more of a “pull” to get it up.
Is sounds like your trolley one wheel each side, and not the triple wheel “stair climbing” type? If your trolley is single wheel, that would be very hard going! The triple wheel is much much easier for getting up stairs, the roll of the triple wheel gives a bit of momentum and there is less resistance. But similarly, the lip on the stair would still make it tricky, but not anywhere near as difficult.