From 《君の名は。 (角川つばさ文庫) (新海 誠;ちーこ)》,
My inferred translation:
She was a kid with slanted eyes and a pony tail who looked like she was around 10 years old and cocky.
But I don't know what role ちの plays or how it changes my translation.
There is also no usage found for this vocab word on jisho: https://jisho.org/search/%E3%83%84%E3%83%AA%E7%9B%AE%20%23sentences
But I did find two usages for 目がち: https://jisho.org/search/%E7%9B%AE%E3%81%8C%E3%81%A1%20%23sentences
However, when I look up verbs for ち I can't seem to find anything that fits with eye (unless I am misunderstanding the sentence): https://jisho.org/search/%E3%81%A1%20