Adding a 4lb will give you approximately 4 more psi, same with a 6lb lower, as long as conditions are optimal. YES, you will need not only a re-tune, but a butt load of supporting mods to handle the additional strain on the cooling & fuel systems if you decide to go this route.
First off, adding a 2.76 upper will only bring the boost up to 15.2 at the very best. This is taking into consideration the atmospheric conditions are just right and you're not experiencing any belt slip. What is the ambient temperature outside? The higher the temperature, the lower amount of boost you're going to make. This may account for why you're only seeing 13+ PSI. Additionally, you will only see this amount of boost at the initial hit of the throttle. The Eaton M112 is not a very efficient blower and is not capable of holding high boost very well in stock form, it just wasn't designed for it. As the RPM's climb and you over-spin the blower your boost will actually drop some.
Now if you add a 4 lb or a 6 lb lower you're going to be spinning that Eaton WAY past it's efficiency level in stock form. You're going to have nothing more than a giant heat pump when you're done! You'll be over spinning the alternator too so you'll need to deal with that while you're at it. I highly suggest you look at having the blower ported before adding a lower. Even with a ported blower 16 PSI is about the max you can make and sustain with all things being optimal. That setup (Ported Eaton/2.76 upper/4lb lower) though will require a bunch of supporting mods. Bigger heat exchanger, new or re-calibrated MAF (Mafia, MAF-Extender), bigger injectors, BAP, new pumps, etc.
I would get the blower ported for now and hope your 2.76 coupled with the new port job can still be safely run with the stock fuel system. To safely make, hold, & run 16+ lbs of boost from the Eaton will take more than just throwing a lower on your current setup.
U.M.