I think I have early periodontitis. Does getting teeth cleanings every 3 months help or wear down your teeth?

Help. Treatment of periodontal disease will not wear down your teeth. Mainly because the procedure focuses on cleaning the area between the tooth, gum, and alveolar bone surrounding the tooth. Your main concern with this treatment is saving the teeth by improving the connective tissues that hold the teeth in place. Please follow the treatment plan and diagnosis of your dentist or periodontist.
It helps to a point. It normally won't wear down your teeth. However, just having those cleanings won't help the problem that you already have. You need active care (getting numbed and having something done) and then after that, your maintenance cleanings are tailored to your response to that active treatment. Just cleaning alone can sometimes be like supervised neglect.
Helps. It doesn't erode your teeth it just removes plaque build up that can loosen your teeth and trap infection.