Tsst.
Every wonder what career a character like Cartman might gravitate towards when he grows up? If you said Project Manager then you probably work as a developer too. Pushy, whiny, demanding, self-centered and glad to criticize you while you are working.
Well, the trick is to assert your dominance and become the alpha dev of your team. Not that you want their job, just that you need to assert that you are a confident professional. But unlike Cartman's mom, you can't actually pinch your PM's in the neck. What you can do is assert your own authori-tay.
If your PM has as much willpower to control work intake as a greedy little piggy then you need to take action. Tsst! They need to flip the words around in their title and learn that if they don't want to look bad they need to "manage projects". It's not your fault they promised that the invoicing changes, website updates, database optimization, customer xyz's customizations and anything else they see lying on the ground while walking to their desk, would all be done by Friday; it's theirs. Sit down with them, list the projects they want to accomplish and figure out what you can finish by Friday. Then work out what it will take to accomplish the entire list. They can then take that to whoever they swore their first born to about that Friday deadline and take their lumps. Don't work overtime just because they cry "but maaa-aam, I want you doo eet, whaaa!". You are only reinforcing negative behavior. Overtime should only be allowed in the case of actual emergencies and by emergency I mean that space aliens and the government are somehow involved.
Pretty soon they will get used to actually working WITH you to plan their projects. And with patience and proper manager training, you will win the war and find yourself in an agile shop without a single shot being fired*.
*Or you'll be fired. This is insanity, I am an insane person. If this works for anyone then they should get their own television show.