Why does bass have more “punch” when I stand up vs. sitting?

By standing, you are changing the position of your ears.  Bass modes—where waves are either summing together (increasing in amplitude) or cancelling each other (wave is out of phase)—occur in all directions, including up and down.  These interactions are so complex that there is no formulaic answer— you can only experiment with speaker placement, placement of your chair, try some corner bass traps, or utilize room correction/equalization, or install subwoofers.

You can try the "Sumiko Method" of speaker placement, which is a bit more systematic version of what tonywinga recommends.  If you try it, you will be surprise how much a tiny movement of the speaker will change bass response.  Above all else, proper placement of the speaker or listening chair will have the greatest impact on the sound (and any improvement will be free of cost).  You can find a description by Googling the method and buying a copy of Wasserman's "Duet" (A song called something like "The Ballad of the Runaway Horse" is used to find the best speaker location; you will get sick of the song).

It does make sense to put a rug on the floor between the speaker and the listening position to kill some floor bounce, and likewise, to not put a coffee table in front of the listening position (or put stuff on the table to break up reflections), but this really does not have an impact on bass response; bass waves are not affected much by putting minor obstructions in their way.  But, one aspect of floor bounce is important--speakers are often designed to account for the wave cancellation from floor bounce, so one should be cautious about introducing big changes in height of the speaker or the listening position.