[Jerrrrrrry]

The "weight on one's 'shoulders'/'chest'" is a figure of speech from the psychosomatical relief one may feel when sharing troubles.

Inversely, the "burden" to respond, whether gravitas is implied or not, can be socially-exhausting to some, and not even conjured by others.

People with low self-esteem or self-worth / depressed / self-described "burdensome" people often assume the pity they may solicit costs the other party part of their own emotional well-being - they've burdened them further with expectations of a response or acknowledgement.