Want to see if people agree with me on this being erroneous
...
The sign pointing to 'North Billerica' has the N bigger than the other letters, which is to indicate directionality, like the larger S in south for 3A. Meaning, in a way, it's randomly stating the road goes 'north' to Billerica, not a road to 'North Billerica', therefore making the sign erroneous.
Given the location and the fact that BILLERICA is signed for the opposite direction, I would say that the larger N in the NORTH BILLERICA sign is indeed erroneous and that the NORTH is in reference to the unincorporated village of North Billerica.
When I saw the NORTH with larger first letter and no route number, I immediately thought of the paddle signs on former US 1 in Boston (dating back to before 1990, which were doctored to cover the numeral 1--remember, this was before shields on paddle signs). Those signs that just said "NORTH / BOSTON" with 1 covered over clearly were hiding something. The NORTH BILLERICA sign seems to want a 3A shield, or at least text. 
For the benefit of those not familiar with this area or intersection, this is one case where
1 Picture = 1000 Words
The D6/D8 LGS in question is along MA 129 (Floyd St.) just east of Pollard St. Shortly after Pollard St.; Floyd St. ends at Boston Rd. (where MA 129 meets & multiplexes w/MA 3A northward). The
NORTH BILLERICA legend with the right arrow is intended for Pollard St.
not Boston Rd. (MA 3A).
If one looks at the Boston Rd./MA 3A intersection itself, one sees
these D6/D8 LGS' for MA 3A & 129.
With regards to those old signs along former-US 1 from Boston to Dedham: I believe you're referring to the MDC-spec'd signage near Fenway Park. Such featured mixed-case lettering for the direction cardinals. Given that those & all other signs near/at the former-US 1 corridor well predated the MUTCD standard requiring the first letter of the direction cardinals to be taller than the rest (but still be in
ALL CAPS); there were no signs along that corridor that featured
ALL CAPS direction cardinals with the taller first letter per
this source.