Can my travel companion use my ticket for the extra seat/space?

It's one thing for a passenger to buy two tickets, it's another thing for a passenger to try to give his or her ticket to someone else. I doubt very much you will be able to do so.

First, I think it unlikely that the gate agent would scan both your companion's boarding pass and yours. Maybe if both of you were actually present at the gate, and the flight were very empty, and the gate agent very accommodating, maybe you could make a compelling case. But allowing it sounds like a security risk, and a frequent flyer mile fraud risk as well, because the account on your ticket would collect miles even though you are not flying, which is generally disallowed.

Second, even if you checked in and your companion didn't attempt to have both boarding passes scanned, the seat isn't guaranteed to remain empty. The main thing that prevents them from giving your seat to someone else is for you to sit in it. Shortly before the boarding process ends, the gate agent will see the list of seats whose boarding passes have not been scanned, and start giving them to standby passengers. And right before the door closes, the flight attendants will perform a count of the passengers on board, and they will note any unaccounted-for seats.

But the basic flaw in your plan is that you don't have the right to give (barter, sell, etc.) your ticket to another person. Your companion would not be recognized as having any claim to your seat or storage. The seat belongs to the airline, and when you purchased your tickets, you agreed to their Contract of Carriage which almost certainly states that the tickets are non-transferable.

This is a big reason why, unlike tickets for sporting events or music concerts, you don't see people trying to scalp tickets to last minute travelers. (And also why there are so many questions at TSE about trouble with wrong names being entered on tickets). Delta's Contract is explicit:

100D. Tickets are not transferable, but the carrier is not liable to the owner of a ticket for honoring or refunding such ticket when presented by another person.

100F. … Presentation of a ticket for transportation on Delta by someone other than the passenger named thereon renders the ticket void. Such ticket will be subject to confiscation and will be ineligible for any refund.

American's Conditions of Carriage state

American has the right, in its sole discretion, to confiscate any ticket … which has been improperly presented or presented by someone other than the passenger named on the ticket.

Tickets are valid for use, reissue or refund only by the passenger named on the ticket. Unless otherwise indicated, tickets are not transferable. American is not liable to the owner of a ticket for honoring or refunding a ticket presented by another person.

United is much the same:

6G. Tickets are not transferable unless otherwise stated on the Ticket at the time it was issued.… Presentation of a Ticket by someone other than the ticketed Passenger renders the Ticket void, and UA is not liable to the owner of a ticket for honoring or refunding such ticket when presented by another person.

and goes on to label anyone to attempts to use someone else's ticket as an “unauthorized person.”

The fact that you want your friend to have the seat is not relevant, because you do not have the right to provide it to another person. It's in the airline's interest, meanwhile, to accommodate as many standby passengers as possible, so they will want to give your seat to one of them.