From BiblePortal Wikipedia

King James Dictionary [1]

SINCE'RE, a. L. sincerus, which is said to be composed of sine, without, and cera, wax as if applied originally to pure honey.

1. Pure unmixed. As new-born babes, desire the sincere milk of the word. 1Pet.  2. A joy which never was sincere till now. There is no sincere acid in any animal juice. I would have all gallicisms avoided, that our tongue may be sincere. This sense is for the most part obsolete. We use the phrases, sincere joy, sincere pleasure but we mean by them, unfeigned, real joy or pleasure. 2. Unhurt uninjured. The' inviolable body stood sincere. 3. Being in reality what it appears to be not feigned not simulated not assumed or said for the sake of appearance real not hypocritical or pretended. This is the present use of the word. Let your intentions be pure and your declarations sincere. Let love and friendship be sincere. No prayer can avail with a heart-searching God, unless it is sincere.

Webster's Dictionary [2]

(1): ( superl.) Honest; free from hypocrisy or dissimulation; as, a sincere friend; a sincere person.

(2): ( superl.) Being in reality what it appears to be; having a character which corresponds with the appearance; not falsely assumed; genuine; true; real; as, a sincere desire for knowledge; a sincere contempt for meanness.

(3): ( superl.) Pure; unmixed; unadulterated.

(4): ( superl.) Whole; perfect; unhurt; uninjured.

Hastings' Dictionary of the Bible [3]

Sincere . The Eng. word ‘sincere,’ as it occurs in   1 Peter 2:2 ‘the sincere milk of the word,’ is used in its old sense of ‘unmixed,’ ‘pure’ (RV [Note: Revised Version.] ‘without guile’).