People use the term differently, when I say sweet spot, I'm referring to the portion of the velocity curve, surrounding the peak of the curve, that contains the shots within the range of velocity that you are willing to accept. So currently, based on what you posted, you consider your current sweet spot to be between 2800 and 1950.
Spring tension and stroke length determine the amount of energy and momentum that the hammer has when it strikes the valve stem. More energy and the peak of the curve moves up in pressure, less energy and the peak moves down. So if you want to raise your starting pressure, increase spring tension or lengthen the stoke, and to lower it, decrease them. You can achieve the same peak with a short stroke and a high spring tension, a long stroke with a lower spring tension, or with many combinations in between. I generally find a shorter stroke and higher spring tension to result in more efficient strings (less wasted air).
Once you get the peak of the curve where you want it, use the metering screw (velocity adjustment) to control the velocity and flatten out (squish if you will) the top of the curve. The more you flatten the curve ( and lower the velocity), the more shots you will get within a reasonable velocity spread.......Higher velocity=fewer usable shots, lower velocity=more. Also as you lower velocity, your sweet spot will expand....just think of it as chopping off the top of the curve.....the more you chop off, the wider the flat spot is. Even though velocity curves are generally plotted as velocity vs. shot number, pressure is fairly linear with shot count so you can think of it as velocity vs. pressure if that helps you visualize it better.
As for pellet weight, heavier pellets are generally more efficient in a pcp so even though you get a reduced velocity (at a given tune) you actually get more energy (FPE) and will usually get a few more usable shots as well. Basically this is because the heavier pellet resists the flow of air more and reduces the amount of air that can be released during the short period of time the valve is open. This is especially true for higher power/velocity tunes.
So yes, with your current tune, you will probably get a few more usable shots with heavier pellets with more FPE, but reduced velocity.