Strangely enough, canvas and canvass sprang from the same source, the Latin word, cannabis, hemp.
In fact, they were identical words. It is only within the past century or so that we have been using different spellings to indicate their different meanings.
Canvas was originally made of hemp, which accounts for its name. It has always been of various weights or thicknesses, depending upon the purpose for which it was needed.
Thus, five or six centuries ago, it was sometimes woven sufficiently fine to be used as a bolting cloth, that is, for sifting flour after it was milled. From that use of the cloth, the word canvas came to be used as a verb, meaning to sift, examine, or scrutinize.
Then it was not long before it began to be used in a figurative sense, as in speaking of the need for examining or sounding out voters and discussing the qualifications of a candidate. Thus we find that by the middle of the sixteenth century, it had passed to the next step, meaning to solicit support for a certain cause, or to solicit votes.
Then, because both meanings were just as commonly spelled one way as the other, it was decided that the textile should be spelled canvas and that the term pertaining to scrutiny should be canvass.