I'd thin it/layer it at the ends, to lighten it, and try and fringe too. It looks like my hair in that it can just sort of hang there. Mine doesn't wave but it has spectacular kinks when it dries. It takes work to make it looked 'groomed' so I try and have a cut that embraces the kinks and sticky-out bits.
Something that thins it out should help it sit better, and hopefully just embrace the natural wave it has anyway.
Something like this maybe? So let the wave curl the layers out, and have a longer fringe to add some shape?
I've posted (hopefully) a picture on my profile of my rubbish hair. Am due a haircut on Saturday & can't decide what to do with it.
I had a fringe cut at the beginning of the year & am debating having it done again.
I last had it cut into a jaw length bob but because my hair has a wave to it I had to straighten it to make it look half decent & with 2 small children & recently going back to work I don't have the time or energy to devote to it.
Ideally I'd love to be able to accentuate the wave but have no idea how.