For doing a scrappy binding with squares this small, you'll have to do a straight seam (although in any other situation I'd do a bias). Reduce your stitch length, use a neutral thread and press seams OPEN to reduce bulk then it will be fine. You might want to try and prejudge at what point you're turning corners too (unless you pre-pin which I don't!) as it will be tricky to avoid a seam at the corner when it's this scrappy.