Sorry, but this is a 'how long is a piece of string' question. Variables:
Size and shape of the canopy. (Yes, sides will require greater weights)
Nature of the site (exposed, sheltered)
Speed of the wind.
However, all is not lost:
If you are car camping, having a set of buckets in the car is an easy way to deal with this. Most sites will have a water supply, and you put somewhere between 1/3 and full buckets and use them as weights. You also create a water supply for quick fire suppression.
For backcountry use, the last thing you want is more weight. One approach is to take any moderately tough fabric (worn out nylon pants work well for this) and sew a loop to an edge. This loop can be tied to an anchor point on the canopy, and anything local can be placed on the attached fabric. Rocks, logs, packs, children engrossed in video games, hibernating bears, petrified dogs...
My usual variation on this is to leave 4-6 foot chunks of small diameter (3/32 to 3/16) nylon rope tied to strategic points then tie these to above heavy objects. You will need to practice a bit for using rocks, as a smooth rock is difficult to tie.
Another variation, depending on the canopy frame is to use a single tiedown from the centre of the frame. Sometimes you can use an existing object in the camp for this. Stumps work well. Fire pits with grate work well if you aren't going to make a fire.