The Collaborative International Dictionary of English v.0.48:

Principally \Prin"ci*pal*ly\, adv.
   In a principal manner; primarily; above all; chiefly; mainly.
   [1913 Webster]

WordNet (r) 3.0 (2006):

principally
    adv 1: for the most part; "he is mainly interested in
           butterflies" [syn: chiefly, principally, primarily,
           mainly, in the main]

Moby Thesaurus II by Grady Ward, 1.0:

18 Moby Thesaurus words for "principally":
   above all, at bottom, basically, chiefly, especially, essentially,
   first and foremost, fundamentally, in essence, in the main,
   largely, mainly, mostly, on the whole, overall, particularly,
   predominantly, primarily