Muhammad DIDN'T marry a 9 year old.
He married a 6 year old and had full, penetrative sex with her when she turned 9.
That is Talmudic influence
MISHNAH. WHEN A GROWN-UP MAN (7) HAS HAD SEXUAL INTERCOURSE WITH (
A LITTLE GIRL, (9) OR WHEN A SMALL BOY (10) HAS INTERCOURSE WITH A GROWN-UP WOMAN, OR [WHEN A GIRL WAS ACCIDENTALLY] INJURED BY A PIECE OF WOOD (11) — [IN ALL THESE CASES] THEIR KETHUBAH IS TWO HUNDRED [ZUZ] …
— Babylonian Talmud, Tractate Kethuboth 11a
GEMARA. Rab Judah said that Rab said: A small boy who has intercourse with a grown-up woman makes her [as though she were] injured by a piece of wood. (1) When I said it before Samuel he said: 'Injured by a piece of wood' does not apply to (2) flesh. Some teach this teaching by itself: (3) [As to] a small boy who has intercourse with a grown-up woman, Rab said, he makes her [as though she were] injured by a piece of wood; whereas Samuel said: 'Injured by a piece of wood' does not apply to flesh. R. Oshaia objected: WHEN A GROWN-UP MAN HAS HAD INTERCOURSE WITH A LITTLE GIRL, OR WHEN A SMALL BOY HAS INTERCOURSE WITH A GROWN-UP WOMAN, OR WHEN A GIRL WAS ACCIDENTALLY INJURED BY A PIECE OF WOOD — [IN ALL THESE CASES] THEIR KETHUBAH IS TWO HUNDRED [ZUZ]; SO ACCORDING TO R. MEIR. BUT THE SAGES SAY: A GIRL WHO WAS INJURED ACCIDENTALLY BY A PIECE OF WOOD — HER KETHUBAH IS A MANEH! (4) Raba said, It means (5) this: When a grown-up man has intercourse with a little girl it is nothing, for when the girl is less than this, (6) it is as if one puts the finger into the eye; (7) but when a small boy has intercourse with a grown-up woman he makes her as 'a girl who is injured by a piece of wood,' and [with regard to the case of] 'a girl injured by a piece of wood,' itself, there is the difference of opinion between R. Meir and the Sages.
— Babylonian Talmud, Tractate Kethuboth 11b
There is lots of references like this in the Talmud. The idea is that physical maturity is what accounts for woemn and not mental maturity.
Sunni Islam simply traced their tradition to Muhammad to give it authority while Shias (who do not believe Aisha was 9 when she married) traced their tradition to the prophet's household while Judaism to some Rabbinic authority.
All of them believe that mental maturity is not needed and physical maturity is what is needed. They differ in how they raced that tradition. Sunni Islam only recognizes prophetic authority unlike Shias who have 12 Imams and Judaism who believe in rabbinic authority.