I waited so long for an answer that I myself was able to find a solution to this phenomenon!) It is called not "pleasant heaviness", but "deep pressure impact". In the source I found, it is considered on the example of a heavy blanket.
"In America, they conducted several studies and found that the heavier the blanket, the easier it is for a person to fall asleep. The fact is that light touches excite the nervous system, and strong but soft - soothes. This works for most people.
Scientifically called deep pressure on the body. Deep pressure is somewhat similar to massage: it relaxes, gives a feeling of peace and comfort. sensations appear when we are taken in their arms, hugged tightly and tenderly or stroked on the back.We felt the same in infancy when our parents swaddled us tightly: soft blankets and parental hands gently pressed on the body - and we calmed down, it became good, cry more I didn't want to.
With gentle pressure on the body, the brain begins to produce the "happiness hormone" serotonin, which in the dark is gradually transformed into melatonin, the hormone responsible for the sleep-wake cycle. A spruce blanket is good because it gently presses on every centimeter of the body at once. We are relaxing, because we received a signal: it is comfortable and safe around, it is time to rest. "
I don't think so. Any severity causes discomfort. When I had a cat, sometimes he liked to come and lie on my chest when I slept. This caused my awakening. Heavy blanket, although warm. still not convenient.