A third of the women is fat?
A third of the woemn are fat?
Fractional expressions such as half of, a part of, a percentage of, a majority of are sometimes singular and sometimes plural, depending on the meaning.
The same is true, of course, when all, any, more, most and some act as subjects.
Sums and products of mathematical processes are expressed as singular and require singular verbs.
The expression "more than one" (oddly enough) takes a singular verb:
"More than one student has tried this."
Some of the voters are still angry.
A large percentage of the older population is voting against her.
Two-fifths of the troops were lost in the battle.
Two-fifths of the vineyard was destroyed by fire.
Forty percent of the students are in favor of changing the policy.
Forty percent of the student body is in favor of changing the policy.
Two and two is four.
Four times four divided by two is eight.
In your case, the sentence would be:
A third of the women are fat.
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