What biological constraints are there on how large a spider can grow?
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 &amp; 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.