I haven't posted much on this site much but I have gone through many versions of my Captain Jack costume. Here is some simple ways to distress it up.
1) the white undershirt- soak in a pot of tea and let dry. This step is time sensitive. Do it too long and you will need to launder it well. Do it a little at a time. If its not where you think it should be, repeat. If you want, put some tea in a spray bottle you can 'dirty' up the cuffs and collar.
2) soak the bandana in a bleach/water solution. Time, trial and error is the key here. Multiple baths can be used. Direct sunlight will also fade it up naturally but it takes time. Make sure you rinse the bleach off and fully dry to gauge how it is lightening up. Don't let a small animal or child get curious and fall into this bath... don't ask...
3) Ideally for the vest you would want the blue darker to start out, but you still may get some results using a bleach/water solution in a spray bottle to fade the middle of the panels like you have been out in the sun for years. Look at reference pics. Then use tea like above in the shirt, or some dry dirt from outside to age and weather the vest. If you wanted to temporarily remove the back panel you could dye the blue darker to enhance the effect.
4) The belts you have I would also rough them up and get them dirty by rubbing them into the ground. You could use shoe polish but be careful and go light. Mine are smooth leather and I used different methods...
5) the sash looks better with a little tea or coffee, near the ends, as over time it would drag on stuff. I had also taken a rasp or sandpaper to rough it up, create holes and make it look ratty.
When weathering, less is more. You can always go further if it isn't enough. It can be tough to go back. What looks like great weathering in person doesn't always show in pictures or film. You can take pictures between attempts and you will see how your costume is aging. I thought I was done so many times and would see a picture of my costume with a fan and I knew right away I needed to go the extra mile.
Experiment, and have fun with it. Sometimes its the accidents that make the best improvements to this costume. There is endless reference pictures online to help you. Hope this helps....
~Jason