If I’m not being pushed from behind, then there is no pushing force.

That's nuts. You can't be pushed from above, or in front, or below - or any other direction than behind?

How is weight a pushing force?

How do you think a scale works? What pushes on the spring/detector/scale platform?

Is something pushing me down from above?

Yes, but that isn't the major source of the weight intrinsic to you. Weight is an intrinsic and inexorable property of all matter. You are made of matter. There is also matter above you pushing down, as well as matter surrounding you on all sides - also pushing onto you.