DS is 8 months old.
My husbands sister has only met him
once when he was 2 weeks old.
There's been opportunity over the summer when lockdown eased for her to come and see him but she didn't suggest it, and neither did we.
Although she doesn't see him, she is constantly messaging my husband asking how "my baby" is and keeps saying things like "I can't wait until all this is over and I
can pinch my baby boy for the night" 
She sends DS lots of things in the post, cards, presents, soft toys etc.
We had a family photo shoot and my husband posted a picture on his social media, she commented "my beautiful baby".
I've posted a few pictures on my Snapchat story recently and have had notifications that she's taking screen shots of them all.
One day last week we were at a farm, she saw the picture on my Snapchat story and replied saying "I hope you're keeping my baby safe"
Last night she sent my husband a picture saying "this is my new tattoo I'm getting"
It was a picture of my sons name with his date of birth.
I know this all sounds harmless, but I'm finding it all a bit OTT and a little strange too.
AIBU to think she needs to back off?