I'm not the best expert for perspective questions, but here's how I understand dealing with heights:
Your background pic has a "horizon line". That's the eye height of the viewer of the background pic. It doesn't necessarily run
through the picture: For instance, if the viewer is looking onto the scene from very high above, then the horizon line will lie higher than the upper edge of the background pic. I'm having good results in my pictures with horizon lines that are around 1/3 from the top.
Impale your person with a broomstick and cut the broomstick so that its top is exactly on the horizon line. Then wherever your person is when it is walking on the floor, it must be proportionally sized down or up so that its broomstick still goes exactly to the horizon line. See below, the horizon line is thick red.
Now if the person is high up, e.g., on a table, then it must have the height that it would have when walking on the floor. (Below, left)
Now his broomstick has become the wrong size. It needs to be adjusted so that its end will go to the horizon line again. When he's walking at the new height level, its proportions will change so that the new broomstick tip still exactly touches the horizon line. (Below, right).
So when a person is climbing a flight of stairs, you can interpret it as if they were climbing a large prism. To find their size at the bottom, stand them on the floor. To find their size at the top, still stand them on the floor, exactly below the top of the stairs and adjust their height there. Then move them to the top of the stairs without adjusting the size.
Corollary: When the flight of stairs is parallel to the front edge of the stage (or top or bottom edge of the background pic) then characters that walk down or up them don't change size. When the "stairs" are a (nearly) perpendicular ladder, then characters using them don't change size, either.
AGS has the concept of "Walking areas" with variable "scaling". I usually deal with that by placing a specific character temporarily into my background picture and finding out how high the tip of their head should measure up to (e.g., it should be just as high as the top edge of that vase in the background). Then I place the character downstage in the room and dink with the max scaling of the walk area until it's about right, i.e, the tip of the head is as high up as it should be. Then I repeat that with the character placed upstage and the min scaling. It's a hassle, but manageable.