The っ or つ in (っ˘ω˘)っ are little arms reaching out for a hug. Put two of them — (っ´▽`)っ — and you're wrapping someone right up.

The ⊂ and ⊃ in ⊂(´• ω •`⊂) are big enveloping arms — the whole-body hug. Bigger brackets, bigger squeeze.

A trailing ♡ like (っ´▽`)っ..♡ is the warmth you send along with the hug. It's a hug you can feel through the screen.

Japanese add ぎゅーっ (gyu~tto), the sound of a tight squeeze. Written beside a hug kaomoji, it makes the hug feel real and snug.

Hug kaomoji are made for comfort — sent when words fall short. (っ´ω`)ﾉ(╥ω╥) is one face reaching out to another who's crying. Pure support in a line.