The stiffness of the line, type of cover and any coatings would affect the minimum size sheeve required for proper functioning.
A bigger sheeve usually runs line better.
Per Harken, the 3" blocks are designed for a maximum line size of 7/16".
They are at least a little oversized for a 3/8" line.
Most of the newer boats I have seen, Tigers, Foxes, Inters etc. use 57mm/2.25" blocks, some with 3/8" line, some with 7/16" line.
I use 7:1 40mm Carbo blocks with 5/16" Vectran and it runs great.
Both 40mm Carbo blocks together weigh 25.9oz./734gm. 50 feet of 5/16" Lite Speed weighs 16.6oz./472gm. For a total of 42.5oz./1178gm.
A Harken 3.00" base quad(#064) weighs 33oz./936gm. by itself. A triple w/becket(#070) weighs 21.5oz/610gm.

There is a catch 22 about blocks and line size, the cleat.
While the 40mm Carbo blocks are rated for 3/8" line, the Harken carbo cleat(#423) cannot handle 3/8" line.
I had to switch to the Ronstan carbon cleat(#RF5000), it is stronger, cheaper and handles 3/8" line.
The 57mm Carbo blocks come with the carbo cleat(#365) which is only rated for 3/8" line, while the Ronstan is rated for a 1/2" line.