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に似てきた

have come to resemble

→ に
phrase Rare #34,551
have come to resemble に marks who or what someone has come to resemble; きた indicates a change that has happened over time.
JA: 妹は最近、母に似てきた。
EN: My younger sister has come to resemble our mother lately.

君だんだん圭ちゃんに似てきたよ

You're starting to look more and more like Kei-chan.

— 天気の子 (2019)

誰かに似てきたと思いませんか？

Don't you think you're starting to look like someone?

— ロード・オブ・ザ・リング／二つの塔 (2002)

二人とも大人になって父さんに似てきた

You both have grown up and started to look like Dad.

— グッバイ、レーニン！ (2003)

だんだんママに似てきたわね

You're gradually starting to look more and more like your mother.

— 箪笥＜たんす＞ (2003)