anyone?
Help me understand Chess Piece Sizes (No. 4, No. 5, No. 6, etc)

Where are you getting these designations? (e.g. "No. 3") I've never heard of chess piece sizes corresponding to a numbered system like that.

Here are some examples:
Weigle # 5: https://www.amazon.com/Staunton-Tournament-Chess-Pieces-Wegiel/dp/B000Z9G456
#6: https://www.chesshouse.com/products/3-3-4-standard-staunton-chess-pieces-6

Yes it's based on the king height and square sizes. The only one I pay attention to is No6 which is basically tournament size. (K3.75 / Sq2.25)

The Staunton scale : ( slight variations up and down are normal and accepted)
size in mm in inches
St. 00 55 mm 2 "
St. 0 60 mm 2 1/4 "
St. 1 66 mm 2 1/2 "
St. 2 70 mm 2 3/4 "
St. 3 76 mm 3 "
St. 4 82 mm 3 1/4 "
St. 5 87 mm 3 1/2 " FIDE size 1
St. 6 94 mm 3 3/4 " FIDE size 2
St. 7 100 mm 4 "
St. 8 106 mm 4 1/3 "
St 9 112 mm 4 1 /2 " ( = "Club size")
St. 10 118 mm 4 3/4 "
St. 11 124 mm 5 "
St. 12 130 mm 5 1/4 "
St. 13 136 mm 5 1/2 "
St. 14 142 mm 5 3/4 "
St. 15 150 mm 6 "
St. 16 160 mm 6 1/2 "

Although some places would accept no5/k3.5, its best to stick with no6 for any sort of competitive play.
Especially for Club play since they go by the official rules which is height 3.75 with base 1.5.
So far i would say yes to the retailers using the number scale accurately.

Oh wow- thank you!
And which Staunton #'s are acceptable for club play? Just 5 and 6?
#6 and #7
5 & 6 for FIDE:
https://www.fide.com/FIDE/handbook/Standards_of_Chess_Equipment_and_tournament_venue.pdf
4 is also accepted in some cases.

more perspective on chess piece vs chess board sizing....
https://www.chess.com/forum/view/chess-equipment/a-system-for-sizing-chess-pieces-and-boards-long

Chess Set Sizing - Pieces vs Board...
The primary sizing criteria for the set and board is that of square size vs King base diameter...
A good rule of thumb is...
King base diameter = 0.75 * square size
or equivalently....
Square size = 1.33 * King base diameter
Any variation from these ratios, or the size of individual pieces and pawns is a matter of personal preference...
http://blog.chesshouse.com/how-to-select-the-right-size-chessboard-for-pieces/
There seems to be a standard sizing system, especially with Staunton style pieces, but I'm having trouble finding a good description. What's the rule? What does No. 4, No. 5, No. 6, No. 10 designate? Is it always the same?
I'm assuming king height...
My best guess...
Am I close?
Thanks!