It does depend on what it is you want to weather, and what material it's made from.
For fabric, I've used spray paints, lightly misted - white (to look worn/faded), browns, black (don't be too heavy handed with the black though). I've also used ink (diluted) in a spritzer. I then like to rub some dirt, or brown powders over the seams and other areas that your ref pics indicate your costume looks dirty - you will need to fix the dirt though, or it'll rub/wash off. If you need to have raggedy frayed edges, make small cuts with a blade and then rub a wire brush over it. You can use the dremel with the sanding drum on for heavier fabrics, but be careful not to get too close to the edge or you're likely to catch the fabric around the thing. Even rubbing your costume over concrete will make it look pretty rough.
For leather, I fatigue it by bending it in the high stress areas (eg look at where your belts wear), and then I sand it along the edges etc.
For armour, it's all in the painting technique. Dry brushing, using a wash, or Rub n Buff are useful ways to weather.
Remember that vinyl/faux leather can't be sanded and weathered the same way as leather. You'll just put holes in it and it'll fall apart. You can, however, paint vinyl.
Hope that helps
