For most of our customers, tzitzit thickness is not such a grave concern. But for others, it's important - or even essential.
Until around ten years ago, there were only two options: thin and thick. Then one of the tzitzit strings makers introduced medium thickness. It caught on quickly, and soon just about every tzitzit manufacturer offered medium as well. Today, even niputz lishmah is available in medium. (FYI, standard thin is 50 cm long, medium is 55 cm and thick is 60 cm.)
But the thing is, not every manufacturer's thick is as thick as the next guy's. Some companies make their thick just a smidge thicker than another company's medium. And some make theirs not just thick, but super thick.
A few days ago I was shocked to hear that a tzitzit seller without scruples went and purchased a very large quantity of tzitzit strings from a fairly new, small-scale tzitzit manufacturer. He noticed that the medium was fairly thick, so he packaged and sold it as thick!
I don't know the manufacturers' calculations when deciding what gage to make their strings. My guess is that it's a combination of economics and marketing strategy. The wholesale tzitzit strings market has stiff competition. On one hand, wool is expensive, while on the other hand the manufacturers know they have to keep their prices down or retailers will look elsewhere. Some are more (or less) generous in the thickness, and some are more (or less) generous in the length. Seems they are scrimping and saving on wool wherever possible.
The packages are always marked thin, medium or thick (דק or בינוני or עבה), so it's easy to tell the difference. But what if you tossed out the package? It's almost impossible to tell by eyeballing it. I can take a good educated guess. My tzitzit tie-ers, who have held tzitzit in their hands 2-4 hours a day or more for many years, can usually tell. But that's only if they have it in front of them. In a photo, it's almost impossible to know (unless you have other verified tzitzit right next to them in the photo).
Techelet tzitzit strings
All of the above applies to all-white strings. But when it comes to techelet tzitzit, it's a bit different. First of all, they don't make medium at all. And secondly, their thick is not very thick at all, it's almost exactly the same as the medium most tzitzit companies make.
Recently we sent a set of Techeiles Chabura strings to a customer in Monsey. He'd ordered thick. When he got them, he was sure they were thin. Unfortunately, when I tried to explain the above to him, he was not very receptive. "No problem, just take a look at the package and check if you see the word עבה," I suggested. But oddly enough, he said he'd thrown out the packaging.
For years, Ptil Tekhelet's thick strings were close to medium, but it looks like recently they've increased the thickness.
Extra thick tzitzit
Some customers like their tzitzit not just thick, but super thick. For years, Mishkan Hatchelet has been making their strings quite thick. Their medium is just a tad thinner than some companies' thick. And recently we stocked strings made by a company called Chacham, which are even thicker than the Mishkan Hatchelet strings.