You may not see much of a speed increase due to weight. However you will find you'll have more energy at the end of your normal routes and simply want to ride further or more often.
My new bike is not quite 5 lbs lighter than my previous bike, but I have found myself asking where those hills are that use to give me trouble. Then I'd realize I just climbed them a mile back.
I don't know what to say about your back. If you've been riding more upright then back issues or not, getting aero takes some getting use to. Maybe over the course of six or so decent rides.
Now that I'm riding a more proper size road bike I find that I want to be lower and more aero. I'm 63 now and can't even touch my toes. If I strain a little I might can get my hands halfway down my shins. So the things other old people say about being too stiff to ride aero is bunk as far as I'm concerned.