Basic physics isn't my strong point, and fluid dynamics even less, but I can tell you my test cases from about 700 solo jumps, and 150 tandems as the instructor in command.

As you jump your body is falling through a volume of fluid, in this instance air. There is force from the skydiver moving through the volume of air, let simplify this and call it wind resistance.

Our terminal velocity is when our acceleration due to gravity equals the force from falling through the air.

You can alter terminal velocity by changing mass, or you can alter terminal velocity by changing wind resistance. We put weight belts with lead shot on skinny girls with no rear ends so that they can fall at a rate faster than their normal terminal velocity for formations with other people. We also alter our wind resistance by bring in our arms and legs, or changing our altitude (belly to earth versus head down).

Even though we are falling through the volume of air, it as if we have wind coming up from the earth. We call this relative wind, but it isn't actually wind like an updraft or upper winds. This is why you can simulate free-fall in a vertical wind tunnel. Blowing actual air past a body can impart the same force as falling through a body of air on a real jump.

With no drogue tandem terminal is much faster than your typical solo skydiver terminal velocity, fast enough to have opening shock that can injure the jumpers and blow up equipment. The reason being is that we have on much more mass than a solo skydiver, but only slightly more surface area exposed to the relative wind since we are attached front to back.

I can free-fall stable without it, but it does help stability. This is only a secondary purpose of the drogue. A tandem instructor needs to be able to free-fall stable with no drogue, you need to be stable when you deploy it so that it doesn't tangle with the pair.

Here is a second actual proof that I have done in free fall:
If I jump with a regular regulation tennis ball it falls way to slow and then second I let go of it I fall away from it. If I put a small slit in a tennis ball from the same container and fill it with lead shot I can add enough mass to get it to fall at a speed that a skydiver can match. Same surface area, same wind resistance, but the extra mass from the lead shot leads to a much faster terminal velocity.