I like a nice, "hefty" knot, and while I don't have the white dots on Navy, I just got my burnt orange diamond weave today, and the standard 3-fold makes a great knot (IMHO). If you want to make sure, you can tell David to put a little bit of extra material in the knot area (which is what I did).
I have this tie (http://www.samhober.com/flower-silk-ties-en/flower-silk-tie-15.html) and while I don't know if it is similar in weight/texture/"heft", etc. to the navy dot tie, the flower silk tie is also great with the standard 3-fold construction.
If you were going with the one of Macclesfields (I have the Macclesfield Print #114) I might suggest going with a 6-fold (though the 3-fold still ties a solid knot, the silk is thinner than the others I have, and I will probably get a 6-fold if I get more Macclesfields in the future), I think that you should be just fine with the 3-fold on the diamond weave, and very likely fine with the 3-fold on the navy dot tie. I don't know what BB tie you have, but I would find it hard to believe that you would consider the knot "too thin" on either of the two ties you plan to buy in 3-fold (though YMMV).
Thanks for your suggestion.
I do have both swatches on hand. The navy pin dot one actually has two layers, feeling more thick and stiff than the dimond weave. I guess 3-fold is good engouh for me. I will talk more about details with David.