Implies annoying behavior, often by someone who seemingly doesn't understand social boundaries. He's always following me around and it's starting to get on my nerves.
Pro Tip 2/3
Affection Misread
Sometimes used to show unwanted attention that could be mistaken for care or affection. My puppy keeps following me around even when I trip over him.
Pro Tip 3/3
Exaggeration Alert
Can be used hyperbolically when someone doesn't literally follow you everywhere. My boss keeps following me around with requests; I can't catch a break!