Yes, the hug-me-tight is not exactly popular these days but they were everywhere 100+ years ago. And, no, they aren’t bizarre and villainous contraptions invented by Dr. Seuss. (That would be a lock-me-tight.)
Rather, a hug-me-tight was a close-fitting knitted or crocheted vest (in the American sense of the word) designed to go over clothing and add a bit of warmth. They sound nice. When Lillian Gish presents one to her rich city cousin in Way Down East, the latter treats it like a dead racoon. Oh well, you can’t win ’em all.