Q. Is sizable or sizeable the preferred American English spelling? Our searches have come up with conflicting answers.
A. If your searches give you conflicting answers, you can be fairly certain that there is no significant preference. But a dictionary will tell you whether one is preferred. The entry in Merriam-Webster is this:
sizable or sizeable
and the front matter of the dictionary (or its Help page online) gives this explanation of how to read entries:
When a main entry is followed by the word or and another spelling, the two spellings occur with equal or nearly equal frequency and can be considered equal variants. . . . If two variants joined by or are out of alphabetical order, they remain equal variants. The one printed first is, however, slightly more common than the second. . . . When another spelling is joined to the main entry by the word also, the spelling after also occurs appreciably less often and thus is considered a secondary variant.
Thus sizable and sizeable are equal variants.