Spiders fascinate me, but what intrigues me the most is just how big some spiders can get, which leads me to my question. What biological constraints (if any) would limit how large a spider could grow, given ample food and no predators?
The standard view on this is that the size of terrestrial arthropods like insects and spiders is limited by the atmospheric concentration of oxygen. This is because they rely upon diffusuion of oxygen into the 'blood' or haemolymph via a system of tubes called trachea that open on to the body surface at the spiracles. As the body grows larger the proportion that has to be taken up by the trachea gets larger. Consistent with this is the presence of fossil giant dragonflies, Meganeura dating from the Carboniferous era when oxygen levels were at an all time high. However you will find that if you go to the Wikipedia page for Meganeura that this idea has been disputed, so the answer may be that no-one really knows.
In relation to alternative explanations; a recent paper by Clapham & Karr (2012) compares fossil insect wing lengths and oxygen concentrations to study the historical drivers of evolution of body size. They conclude that oxygen seems to be the main driver until the end of the Jurassic, but after that biotic interactions (such as bird predation) could be more important.
One way spiders could become much larger is if oxygen levels in the atmosphere increased. This happened with almost all land arthropods during the Carboniferous period, when oxygen levels in the atmosphere shot up to 35%, as opposed to a measly 20% today. In pure or near near pure oxygen, bugs, including spiders would reach truly monstrous sizes, and by monstrous, I mean much bigger than you, creatures like plane sized flies, tank sized beetles, spiders the size of houses, etc. This is because of the design of the respiratory system in arthropods, as they rely on a series of tubes called spiracles or organs that are similar to gills, known as book lungs, that work in air. These systems rely on diffusion, and this means there is a cap to the size that a land arthropod can grow to, but this cap moves with the oxygen level, the higher the oxygen level, the bigger the land arthropod can get. So yes, there is a way to make giant spiders.