The Collaborative International Dictionary of English v.0.48:

Meekly \Meek"ly\, adv.
   In a meek manner. --Spenser.
   [1913 Webster]

WordNet (r) 3.0 (2006):

meekly
    adv 1: in a submissive or spiritless manner; "meekly bowed to
           his wishes"
    2: in a humble manner; "he humbly lowered his head" [syn:
       humbly, meekly]

Moby Thesaurus II by Grady Ward, 1.0:

27 Moby Thesaurus words for "meekly":
   abjectly, acquiescently, compliantly, gently, humbly, like a lamb,
   mildly, modestly, on all fours, on bended knee, pacifically,
   passively, peaceably, quietly, resignedly, submissively, tamely,
   unassumingly, uncomplainingly, unobtrusively, unostentatiously,
   unpresumptuously, unpretendingly, unpretentiously,
   with bated breath, with due deference, without ceremony