OA in neck, upper back spasms. Overhead exercise tightens back. Should I try doing overhead exercises or avoid? Weights OK? Flabby upper arms/obese.

OK to avoid them. First it may help to work with a certified personal trainer to modify an overhead exercises so that they are more "tolerable". Otherwise, no exercise that is done overhead is "necessary". Be reassured that you can readily find alternatives that will be suitable without compromising your the benefits you are receiving.