Cheese Molds pre-1600
With many ceramic objects from ancient times (and before) that figuring out how something was used is pretty tricky. It's all guesses unless there is some sort of detailed writings during the time period it was made. Usually every day use of some objects just weren't discussed. We only use modern interpretation of what we know of the uses of the object and any other documentation we may have from previous sources. Analyzing the object for any residue, such as various food compounds, help with identifying what the object was on contact with. That helps in the identification process.
Ancient cheese molds are actually a fairly interesting object. Faisselle (Cheese strainer) is another name for a bowl with holes to allow whey to drain from the curd. They come in different shapes and sizes. The word comes from the Latin fiscellae. These strainers were originally made from bisqued clay, stoneware or porcelain, and later in wood, iron, aluminium, and plastic.
Two more related words: FAISSELLIER : instrument used for pressing curds in Neufchatel cheese.
FAISCINE : (related to Faisselle, Latin origin) meaning a whey mold, used in the region around Tours.
These molds (moulds) could have had some sort of weight added to them. Adding weight would make them presses, but as there hasn't been any pieces found that would fit within the mold as a press, it's difficult to rule that use in or out. Perhaps they stacked on top of one another, however usually if there is a stacking pot, the foot and lip are adjusted in the creation so that they "lock" in place making them more stable. I haven't seen the underside of any of these pieces, so it's though to say if that was done. From what I can see the lip is flat and the walls are straight. So, while they could stack, boy they would be easy to knock over.
Since none of the potters are alive that made these pieces, its really tough to say why they did what they did. Pottery even in ancient times was fairly advanced. Ceramics haven't changed a whole lot since the wheel was created (save a number of firing and some other techniques which came from leaps of technology in various areas of mining and production).
These are the main shapes that were locked into "cheese molds" but other items can be used for the same thing. Late period, in Brittan, there were colanders that looked very close to an illumination which shows cheesemakers. The archeologists aren't always right. Anything with holes can be used as a mold and if you can fit in weights, a press.