Does and area rug on top of wall to wall carpeting make a room look smaller or bigger?

I think that would depend on the color of both the rug and the carpeting. JMHO

I would not put a rug over carpet when showing your home: it's not necessary. It's a possible trip-hazard. And, it might generate suspicions among buyers as to what the area rug is hiding, thinking there may be soiled or damaged areas on carpeting, for instance, whether that is true or not.

You want to keep things as uncluttered as possible and not distract buyers with your decor. Your room will look more spacious with clear sight lines on the floor and walls.

Sage advice Aychi.

It sounds like you posted about resale under another thread? If so, I agree it will look as though you're concealing soiled or damaged carpeting to a perspective buyer.

If resale isn't on the table, then it's fine to use an area rug atop carpeting particularly in a dining space to protect the wall to wall.

If the hue value of both flooring isn't too stark a contrast, the carpet will act as a boarder to the area rug if the area rug isn't too much smaller than the wall to wall. In that case, it won't enlarge or shrink a space.

Using an area rug atop wall to wall in the case of a rental property can be a G@dsend in the case where the wall to wall is in poor shape or the wrong color for your room scheme. Having a rug remnant bound can be a frugal way to create an area rug.