The model of a warp-weighted loom is a significant part of the textile production display as it presents a physical, tangible example of how weaving is done. I've noticed that for non-weavers (so, most of the population!) even the most basic description of the process leaves them with glazed eyes and nodding heads that tells you that, while they appreciate you trying to explain weaving, they really don't get it. A working model of a loom, however, lets them see instantly the interplay of warp and weft threads and thus the process of weaving becomes clear.
Wow, that was one pompous paragraph! Now, to the nitty-gritty: I decided to make the warp-weighted loom first (a model of a horizontal 4-heddle floor loom is scheduled for next season, 2010), because it was simpler to put together and I had all the necessary timber on hand. The side pieces of the loom are made of maple (because it's less likely to warp out of shape over time) and the front and back bracing are of pine, because I had some scraps the right size lying around; the pegs that hold it all together are an unidentified softwood dowel that I picked up in a craft shop to make spindle shafts out of, and the roller is tassie oak (an offcut from the tent poles). The warp is 2-ply handspun brown wool - not sure what sort of sheep it came from, but it has a 5-6 inch staple and is pretty coarse; the weft is a similar wool but in white. I chose a traditional 'goose-eye' weave because it is period, and pretty...
Setting the loom up is basic but time-consuming: First the warp needs to be cut to size (in this case a metre long) and then looped onto the roller. Then each warp thread is fed through a small figure-8 of thread on the heddles - the pattern in the fabric depends on how these are threaded (in this case 1-2-3-4-1-4-3-2) and then the ends of the warp are tied to clay weights (these are made of an air-drying clay, suitable for display purposes but probably too fragile for a loom used for real weaving) in groups according to which heddle stick they are fastened to. This ensures that when a heddle stick is lifted, all the warp will remain under tension. The chaining of the warp occurs so that there's enough warp available to weave a decent length of cloth - as it's woven and rolled onto the roller at the top of the loom, the weighted ends rise and eventually would reach the heddles and any more weaving would be impossible. This way the warp can be 'lengthened' by undoing and re-doing the chains so that the weight can remain near the ground and the fabric can be woven as long as possible.
Then it's a matter of wrapping some weft around a shuttle and weaving - the order the heddle sticks are lifted affect the pattern too - in this case it's 4/1-1/2-2/3-3/4-4/1-3/4-2/3-1/2. Each line of weaving needs to be beaten into place (so it lies straight) with a weaving sword, which is a flat, straight piece of wood with a tapered edge (traditionally they were also made of metal - a lot of them look like large, blunt cook's knives with a wooden handle), then the heddles are changed and the next line of weaving occurs.
It's a slow process and hard on the arms, but cloth was woven in this manner from the last ice age up until around the late 12th century when the horizontal floor loom made it's appearance (horizontal looms are mentioned in an 11th cenury Arabic text, but its unclear as to whether they were the mechanised, treddle sort). The main advantage of the warp-weighted loom, than as now, is it's portability. The top roller is lifted off the side pieces, along with the heddle sticks and clay weights, and the entire thing laid out flat on cloth and then rolled up. The roll and the side pieces can then be transported and then set up again, ready to weave, without any difficulty. A horizontal loom is very much a fixture and must be moved in toto if it has weaving on it, or the heddles and reed must be re-threaded up on setting it up again.