Cute or creepy?

My sister is my best friend. This woman has been there for me always. We were both ttc, but I got pregnant. Oh you should have seen how happy she was! She immediately went out to get me roses and bought baby cot(no joke)! She insisted on getting necessary nursery items, even when I told her that it was fine. She’s everything and more that one could want from a sister... I love my sister so much that I begged my husband to allow us to name our girl my sister’s name. My sister has been my rock... she takes my daughter like hers and I mean it! But it’s now freaking me out... I would go out with my sister and baby and my sister would introduce my baby as her baby. She uploads pictures everywhere of my baby, she takes my 8 months old to hers and beg that baby girl spends 2 days with her, I always agree... matter of fact my sister made a nursery room in her own home for my baby. Now here’s the thing, yesterday we were together and my sister was playing with my baby as normal, but what caught my attention was that my sister kept telling my baby “mama mama. Mama loves you. Come to mama. You are mama’s favourite girl”... constantly referring to herself as my baby’s mama. I know this is supposed to be cute, but it’s creeping me out!