Today I have been doing research clothworkers in England. It is a possibility that Walter Chiles could have been a member of the "Worshipful Company of Clothworkers" in England. Most clothworkers served as apprentices for seven years. So this could be a door to the identity of Walter Chiles in England, but I believe that it will take a visit to England to find your information. He became the assistant purser on the Blessing in 1637. Could this be because of the economy? There was a depression during 1637 and 1638, but I have yet to know the full details. This could very well be why he left his profession of clothworker to start a new life.
The Worshipful Company of Clothworkers has some records. Some from the 1500s, mostly 1600s forward.
The Worshipful Company of Clothworkers was incorporated by Royal Charter in 1528. The original craft of the Clothworkers was the finishing of woven woolen cloth; fulling it to mat the fibres and remove the grease, drying it on tenter frames (from which derives the expression "to be on tenterhooks") raising the nap with teasels and shearing it to a uniform finish. The Ordiances of the Clothworkers Company, first issued in 1532 and signed by Sir Thomas More, sought to regulate clothworking, to maintain standards and to protect approved practices.
Below I have attached links that may be of some help in your research:
There are quite a few books on the clothworkers on google e-books which may be worth reading for a more expanded few of the clothworkers lifestyle and the decline of the clothworker in England.