We are talking about the vang? The blue line is in a 6:1 purchase. That is, the force on the line is 1/6th of the force applied to the orange line. The orange line is a 2:1 cascade, so the force on the boom is 2 times the force on the orange line, or 12 times the force on the blue line.
For a short pull, I can manage 40 pounds even on a 4mm line. Usually, I think I pull at most 10-20lbs when I adjust the vang. Say, 50 lbs is the absolute ceiling. Then, the force I apply to the line is 50, the orange line sees 300 (it's 3/16th) and the boom sees 600.
In my estimate, the weakest link is the SS strap on the boom. All the ropes are within spec (for reference, the orange line is Samson ultra-lite, and per their specs it rates 1200 lbs, or 600 after things like knots. They don't say whether they list breaking strength or SWL, so I assume the former. I estimate it gets loaded to 300 at most, which would leave a factor 2).
At 14knots wind pressure is about 1lb/sqft. With a typical DS main, the total wind force on the main should be 100lbs, (factor 4 or) 400lbs if it gusts to 28knots (factor 2). Somewhere along this curve, you end up exceeding the righting force from the crew hiking - that force is the maximum load on the sail because after that, you capsize.
With a beam of 6', and crew weight (fully equipped) of 400lbs, you can get 4' x 400lbs or 1600 lbft. Assume center of effort of the sail at 10', and you can hold a sail force of 160 lbs! I think the actual number is a bit higher, because the boat, when heeling, doesn't do that around its centerline, but I don't think the distance between center of buoyancy and center of mass ever gets to be much larger than 5'. In that case you can hold 200lbs of sail force.
Because of vang location and angle, the vang takes higher forces than the main sheet. You loose about 50% from the angle, and another 50% from the distance, so your vang needs to pull 4 times as hard as your mainsheet, assuming center boom sheeting. With a 4:1 mainsheet, pulling 35bs on the free end would get you 150lbs of pull on the center of the boom. With that estimate, you get the same pull on the boom, as with 600 lbs of vang tension (accounting for the fact that the main sheet and vang don't pull in the same direction (it pulls in and down), you need to pull a bit harder on the main to get the boom equally far down, so now you get to 40~45 lbs on the main sheet.
Unlike a vang, you'd hold that continuously, and that's where ratchet blocks come in
I don't get to sail my DS at the upper end of the wind range often enough, but I know I can manage to hold the mainsheet in hand when it blows into the 20's. But I use 3/8" and a ratchet block.
So running all these numbers, the vang strength should be just about adequate for the extreme case where the entire sail force counterbalancing the maximally hiking crew is held by the vang only. (In reality, the jib takes a good share).
Let me know if you spot any flaws in the reasoning so far.