Because it fit the name.
Louise Jameson herself, the actress who played Leela, did an interview with Doctor Who Magazine in which she answered this question. The interview is reproduced on the interviewer's blog (emphasis mine):
To begin with, Louise wore contact lenses to make her blue eyes look brown. In pictures from an early make-up test, her skin looks very dark. Was Leela intended to be the show's first black companion? It was still fairly common for white actors to "black up" – in Leela's third story, The Talons of Weng-Chiang, the white actor John Bennett was made up to look Chinese.
Louise is candid. "It was never specified with Leela. Quite honestly, in those photos I think the make-up woman just didn't get it quite right. The dark eyes were because, I was told, Leela meant 'dark-eyed beauty'." Again, she considers. "There was always an hour and a half in make-up before I was allowed on set. I wasn't black but it was more than a tan. One of my sons is mixed race – dual heritage we say now. I think I was meant to have that kind of skin."
I checked a few sources and couldn't find any reference for Leela (or related names like Leila) meaning specifically someone with dark eyes, but the name is definitely related to darkness: The Bump says it means "night beauty", Wikipedia says it refers to darkness or night, and Baby Name Wizard says it comes from the Persian for "dark-haired". Anyway, the connection with darkness in general is enough to justify the decision to make Leela a dark-eyed character.
Interestingly, the actress didn't know (at the time she was playing Leela) the specific origins of her character's name, after the Palestinian Leila Khaled:
Indeed, she was named after a terrorist who'd been in the news – Leila Khaled of the Popular Front for the Liberation of Palestine.
"Oh really?" laughs Louise.
She didn't know?
"Certainly not back then. I based Leela on a three-year-old who lived upstairs from me and on Bosie, my then dog."
