Do I need an upgraded meter base when changing 100 amp service to 125?
Yes, but only if the meter base isn't already 125A.  I find it curious that they'd run 1/0Al when #1 would have sufficed for a 100A seevice.  It was like someone intended to go to 125 later.  Perhaps this same thinking guided the selection of the meter base.  

Now,  as far as that service panel.  Far and away the most painful thing about changing a service panel is physically fitting all the cable entries and conduits to the edge of the box proper.  Yet, the working innards are what makes a panel 100 vs 125A, main vs sub, 2-pole vs 3-phase etc.  But think about it.  Manufacturers make hundreds of panel sizes but only a few box sizes.   

So it's worth the legwork to see if the manufacturer can sell you a box with the guts you need that fit the same bolt pattern on the box you have wired-in.