Take
XLS Yacht braid a typical double braid polyester rope that you might use for a halyard if you aren't being fancy.
Strength for a 3/16" starts at 1200 pounds and goes up by about 1,000 pounds per 1/16". By 5/16" we have reached 3,300. That's ultimate strength. For working load, you'd divide by 5, so 3/16" gets you 240# and you gain about 200# per step to end up with 660# for the 5/16". From that perspective, 1/4" doesn't look too bad with 440#.
Now, what about stretch. XLS is not the most low-stretch rope you could get, so it stretches 1.5% at 10% of strength and 2.2% at 20% of strength. Because we assumed 20% as our maximum safe working load, we get less than 2.2% of stretch if we stay inside those conditions.
The maximum actual load on the halyard is estimated by how much wind force it takes to capsize a DS with fully hiked crew. Any higher wind pressure would not lead to higher loads, but simply capsize the boat. Allowing for shock loads, it may be possible to exceed 240#, but 440# seems unlikely and 660# seems a real stretch. Bearing in mind this is just an estimate of likely values, and not a detailed calculation, the 1/4" still looks comfortable.
Back to stretch. If we dimensioned our rope the right way, we might expect that a typical gust reaches 1/2 the working load, and with a factor 5, that's 10% of rope strength and for XLS that would be 1.5% stretch. Between 1/4 and 5/16, the working load goes up by 50%, so the stretch would go down by a third (to 1%). However, the stretch isn't fully linear, otherwise 10% of full strength (half working load) would have .7% of stretch and not 1.5%. This is probably due to the effect of "construction" stretch vs. "fiber" stretch. At first, the braid is pulled tight, then the fibers themselves get stretched.
So, increasing the size further, would just put us in the region where the initial stretch is not enough to pull out the construction stretch. If the loads are sized right for 1/4, going to 5/16 gives some improvement, but if the loads in fact allowed 3/16, going to 5/16 might not improve matters over going to 1/4.
As a result, I see no benefit to providing for 3/8" sheeves...
If you want lower stretch, the way to go would be to upgrade to XLS Extra, where you get 10% more working load with only 1/3 the stretch. For that rope, 1/4" is definitely good on both the load and the stretch.
Or you could use
Amsteeland have the same .5% stretch and 500lbs working load with 1/8" diameter. And it's 5 times lighter...and way easier to splice.
You can combine the Amsteel with another line of cheaper make, so that the Amsteel will just be long enough to take the full load and the other part of the line is only used in hoisting the sail - that's what I ended up with after I initially used 5/16" XLS for several years.