But if the cardinality of the sets are equal, as is the case in each step of the solution, the set containing the max-weight ball is necessarily heavier. Can you explain further?
consider the following example where the condition "one ball is heavier than the others" holds true but your method yields the wrong solution: {1,10} vs {6,6}
when it is further specified that all remaining balls are of equal weight then your solution cannot be optimal since comparing two thirds yields the required information about the remaining third.
I didn't downvote you, but I think they object to your overly literal interpretation of "one ball is heavier than the others" given it was contrasted with the original phrasing "one ball is a different weight". This is a math puzzle, not a lateral thinking puzzle.
Not to draw this out further but I do think variations of these make for good interview questions for entry-level people. Here is why:
First, it is trivial to communicate the problem and any moderately competent person will find a solution within a short time frame. Second, it tests how precisely someone takes a problem definition. (In my experience, the kind of person who glances over such details will also tend to make trivial programming mistakes like off-by-ones.) Third, by varying a well-known question slightly you can easily filter out those who have simply learned the "correct" solution from the internet rather than thinking it through.