Scott, I apologize in advance that there is a huge amount of verbiage here, and also that I wrote this for another purpose, but it does explain my thinking.
If I were to give an uncharacteristically (for me) terse explanation of what happens when you increase backstay tension on a modern fractional rig, I would say that increasing backstay tension decreases weather helm and heeling, by flattening the sails, reducing the angle of attack of the upper sail, and as counter intuitive as this sounds, moving the center of effort forward. If you want the short answer, that's it and so stop reading here.
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Still here? Good, because, that summary of the 'whys' does not explain how any of that happens. But to explain how tightening the backstay on a modern fractional rig decreases weather helm and heeling, flattens the sails, reduces the angle of attack of the upper sail, and moves the center of effort forward takes a lot of verbiage, because frankly there are a lot of pieces and parts in motion, and it's the interaction of those parts that tells the whole story. By necessity, explaining how a modern fractional rig functions has enough "Gizmo A pulls on Gadget B which bends Object C's" to make Rube Goldberg proud. But a modern fractional rig is anything but a Rube Goldberg device. It is a highly evolved and sophisticated system which works with surgical precision and a Rolex like synchronization of nearly all of its moving parts working in unison to depower the boat with the singular application of more backstay tension.
So starting at the backstay, no matter what mechanism is used to increase backstay tension, there is a shorting of the dimension between the transom and the masthead. This pulls the masthead aft and downward. In fact, depending on the rig proportions, the force downward will typically be 3-4 times the force pulling straight aft.
And those combined forces move the masthead towards the stern and towards the deck.
And that shortens the dimension from the masthead to the end of the boom.
And that loosens the tension on leech of the mainsail.
And that allows the aft end of sail to twist to leeward.
And that reduces the angle of attack of the mainsail.
And that reduces the side forces on the aft edge of the sail,
And that alone reduces heeling and weather helm.
But that's only the beginning.
What keeps the mast from being pulled over the stern or crumpling to the deck are the forestay and shrouds. The forestay acts as a fulcrum bending the mast in much the same way that your hand on the grip of a bow (i.e. bow and arrow) allows the tension of a drawn bowstring to bend the bow further.
And so in that manner the backstay pulling aft increases the bend the mast, while at the same time pulling the head of the forestay aft as well, increasing the tension on the forestay.
And the bend in the mast and the increased forestay tension forces the attachment point of the forestay slightly downward and back toward the stern.
And that moves the head of the jib closer to clew of the jib,
And that loosens the tension on leech of the jib.
And that allows the aft edge of jib leech to twist to leeward.
And that reduces the angle of attack of the jib.
And that reduces the side forces on the aft edge of the sail,
And that also helps reduce heeling and weather helm.
But that is not all;
As the mast bends, and as we said above, the upper part of the mast above the forestay bends towards the transom. But below the forestay that increased bend actually moves the mast and attached sail towards the bow.
And since there is more mast bending towards the bow than towards the stern, the geometric center of the mainsail is actually moving forward in the boat.
And that increases the proportional center of the forces toward the forward edge of the sail,
And that also helps reduce weather helm.
But that still is not all;
Because, the increased tension on the forestay straightens the forestay and the luff of the jib.
And in doing so the geometric center of the jib is also moving forward in the boat.
And that increases the proportional center of the forces on the forward edge of the sail,
And that also helps reduce weather helm.
But that is not all either;
Because as the mast bends, the masthead moves aft and the upper leech of the sail also moves slightly aft, but at the same time the curvature at the mast moves the leading edge of the mainsail forward towards the bow.
And as the distance between the leech and the luff gets physically longer, the curvature of the sail gets stretched flatter.
And that results in a depowering (flattening) of the sail so that the mainsail now generates less side force relative to its drive.
And that depowering also helps reduce heeling and weather helm.
And we are still not done;
As mentioned above, the increased tension on the head of forestay straightens the curvature of the forestay and so the middle of the forestay moves towards the bow increasing the distance between the leech and luff of the jib as well. In much the same way as the mainsail description above, as the distance between the leech and the luff gets physically longer, the curvature of the jib gets stretched flatter.
And that results in a depowering (flattening) of the jib so that the jib now generates less side force relative to its drive.
And that depowering also helps reduce heeling and weather helm.
And all that combined reduction in heeling, also reduces weather helm.
And that all happens all at once when you tighten the backstay on a fractional rig.
When new sailors hear or read this explanation, they sometimes think. "That sounds way too complex for me to be able to use effectively." But here is the really great news about this, virtually all fractional rigs come with an instrument that tells them rather precisely how much backstay to apply. Its called 'the helm'.
All you need to do to tell how much backstay to apply is to watch and/or feel the helm. As you apply backstay you will feel the force lessen on the helm, and you will be able to visually watch the helm move back towards being neutral, and when you get to the spot where the helm is where it feels or looks about right, you have enough backstay tension. If the boat starts feeling sluggish, you probably have too much tension. Using the backstay adjustment on a modern fractional rig is just that simple.
Jeff