Weights are a little different here than traditional systems, mostly for the sake of simplicity and reading. Main weighted stats can be weighted from 0 to 5. The final score (Pointscore) of an item is calculated based on the addition of all of weight*stat products. Items on the site are sorted by Pointscore. If a class/spec hypothetically has only two weights: intellect and spirit (let's just say int is 5 and spi is 4), and the item we're looking at has 250 int and 175 spirit, here is the Pointscore calculation:
Pointscore = (5 * 250) + (4 * 175)
Sockets are weighted from 0 to 1000 (1000 being closest to a Cogwheel socket, ie ~200 stats from the gem times weight value 5). Anything outside of this range is invalid.
Changing weights is available on all pages for a spec (even the overview). Each spec has its own set of weights.
To change weights, enter your own value (premium only) and hit "Apply" or "Save". The items will automatically be ranked according to the weights. You may reset weights and store your own weights to the site's database (for later use). If you use the site's weights you can still change the values, but they will be reset after a certain amount of time (when you clear browser history or after a few days).