After reading about how Amazon has some scheme to weight reviews based on recency, verified purchase, or helpful votes, I have tracked my Amazon-assigned rating average compared to an arithmetic average of reviewer ratings. My finding (anecdotal, exactly one book): There is no weighting.
The rating average, which is presented in tenths, has faithfully matched the weighted average of user-provided ratings. The hundredths place rounds you up or down to the nearest tenth. For instance 4.55 or better results in 4.6, while 4.54 results in 4.5.
Based on this I think the only impact of Verfied Purchase is that the reader sees the tag and it may affect their perception of the review. The helpful votes matter more because they affect placement of reviews on the page (I think the Most Helpful Critical Review is the most important one), but they do not affect average rating.
Anyway hopefully review-weighting is one less thing to worry about.