You don't weather the figures after painting them--you determine the color from the start. Most common mistake is to paint everything the same color. Even when new, no two items of uniform are ever exactly the same shade unless they came from the same lot of fabric (unusual except for privately-tailored officers' uniforms). As fabric ages, the differences becomes more pronounced. So add a drop of black, white, or any primary color to the base paint color so no two items of uniform are exactly the same color. German Feldgrau wool uniform fabric became noticeably yellowish as it aged (though the 1939 Polish campaign was so short, this wouldn't have happened yet).
Likewise, a painted metal item will never match a piece of fabric, even if the manufacturers were working from the same color chip, so a Feldgrau helmet will not match a Feldgrau tunic. Europa Militaria publishes a series of books showing color photos of real uniforms being worn, and you will get a much clearer idea of the range of colors actually seen.
For ground in dirt, you can mix an earthy color with your basis uniform color and blend it in as you paint. Bill Horan's book on figure modelling shows you how to do this with enamels. Other books show you techniques for acrylics or oils, depending on your preference.