Looking for weighted pieces for 15” Board

It should match the board, have you got picture of the board?

Sets with King diameter of about 27-31mm (1.06-1.22") and pawn diameter of 19-22mm (0.74-0.86") would fit perfectly, depending on your preference for more or less space. You are looking for king size of 68-75mm (2.6-2.9").

These say they are single weighted, https://www.houseofstaunton.com/analysis-plastic-chessmen-2-5-king.html

I have the 2.5 inch plastic analysis pieces from ChessHouse, and they are unweighted. The claimed set weight of the HoS set is the same as the ChessHouse set, so I doubt the HoS set has additional weights. Maybe their definition of single weighted is different from this one that came up when I googled 'single weighted chess pieces':

"Single-weighted pieces have a single metal pellet inserted into them - usually made of iron..."

I'm just mentioning this to help prevent any misunderstanding before ordering.

This probably meets your specification, although maybe a bit cramped compared to Pamvo7's measurements: https://www.wholesalechess.com/the-library-marshall-series-plastic-chessmen-2-875-king.html

Have a look at this set from Muba on Amazon. I like using this set on my 15" board with 40mm squares. It's probably the biggest (3.5") and heaviest (32oz) set that I found which reasonably works with smaller sized boards. This picture gives a good idea of the fit.

To my surprise, I actually received extra queens with my set.

Chess Set Sizing - Pieces vs Board...

The primary sizing criteria for the pieces vs 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, becomes a matter of personal preference...
https://blog.chesshouse.com/how-to-select-the-right-size-chessboard-for-pieces/

See also...
https://www.chess.com/forum/view/chess-equipment/a-system-for-sizing-chess-pieces-and-boards-long

You might also want to consult the FIDE Manual, Sections 2 and 3 on equipment regulations...
https://www.fide.com/FIDE/handbook/Standards_of_Chess_Equipment_and_tournament_venue.pdf

Imo it's too big for that board. If 4 pawns don't fit into 1 square it's too tight, harder to read the board.

That set is ugly and the pawn is too tall and from first sight it's hard to tell the queen from a bishop and from the king.

Wooden sets are all ugly in that price range.

I think it's easier to find a plastic set that looks nice. Look for any 3" king chess set

Example, not perfectly sized but cheap:

https://www.amazon.com/ELONGDI-Weighted-Chessmens-Waterproof-Replacement/dp/B0CM3KCDMY/

And maybe amazon is not the best place for chess stuff

@RussBell Yeah, this is why I think this Muba set works with the 40mm squares. The king's base is right at 30.5mm...perfectly in-line with some discussions that you referenced.

Yes, your King diameter fits perfectly but the pawns are way too big at 26mm diameter. The 40mm board fits 4 pawns with diameter 20mm (for those who prefer more space) or 2 pawns with diameter of 23.4mm (for those who prefer a bit less space), and anything in between is recommended. Your pawns make it too crowded but of course if you like it it's fine for you.

Just add weight yourself . . .

I hear ya @Pamvo7, and I've read several discussions regarding sizing. However, I don't recall many rule considerations when dealing with smaller (non-tournament) boards. I've seen many people disagree with the 'four-pawns-per-square' sentiment (70mm squares for 'Tal' pawns is way overkill). But when sizing for smaller boards... other factors seem to take priority. I don't want to feel like I need tweezers to pick up tiny plastic pawns with hardly any weight. Nor do I want to look at those cheap mold seams. I would much rather have these larger pawns that are easily handled, and with nice wood grains...rather than tiny, light, cheap looking plastic pieces.

I do find it comical that someone just complained about 'four pawns don't fit into 1 square'...and then proceed to point to a plastic set where 'four pawns don't fit into 1 square'.