I have weak chin causing skin irregularity. What is happening that causes my skin to darken and dip in that area?

Thank you for your pictures.  This lack contour/shadow is due to lack of bony support afforded by an appropriately positioned jaw and chin.  I would save money to get the right surgery (jaw advancement possible chin advancement or implant)

Dips or dimples occur like that from a separation in the underlyng muscle layer. In your case and location that would be a split between the depressor anguli and risorius muscles. Be aware that this indentation will not be improved by a chin augmentation and you should not expect that it would.

A chin implant can augment the weak chin profile in both the  frontal and lateral projection, but will not help with dynamic dimples/ or skin changes.  Chin implants are composed of Silastic and are inserted through a sub-mental incision under local anesthesia.  For many examples, please see the link  below

Yes, you have a weak chin which can be corrected with a chin implant.  If you place your finger from your lip straight down, your chin should almost touch your finger.  Yours is fairly far behind.  Adding a chin implant will project the chin forward and balance the lower half of your face.