Fetching details from the dictionary...

to adhere to; to stick to; to cling to
to keep close to; to go along with
to get involved with; to be thick with; to become intimate
飴が手にくっ付いて取れなくなった。
The candy stuck to my hand and won't come off.
ペンキがまだ乾いていなくて服にくっ付いた。
The paint wasn't dry yet and stuck to my clothes.
寒いので毛布にくっ付いて離れたくない。
It's cold so I don't want to leave the blanket.