Thickness is important and there are different strategies for dealing with different thicknesses. But if you're having a problem getting them dry and crisp in the center before the exterior browns too much, there are a few standard suggestions. In order of complexity/extra work:
- Make sure you're frying at an optimal temperature. You might try varying a bit: going a little lower in temperature might allow the chips to finish cooking before they brown too much. But it could also make them greasy or soggy if you go too far, so this may not be ideal.
- Rinse the raw chips in water before frying. This removes some of the surface starches that will lead to faster browning.
- If you're willing to do even more work: After rinsing in cold water, drop the raw chips briefly in boiling water and cook briefly (for a couple minutes). Strain them or pull them out with a large spider before they begin to fall apart. Better yet, add a little vinegar (about 1 Tbsp. per quart) to your water, which will help the chips cook longer without falling apart and will remove even more surface starch. Let them cool and dry for a few minutes before frying.
For more details on the last two tips, see this article at Serious Eats (which contains photos of the results).