The phrase "Vast weight" is correct and usable in written English.
It can be used to describe something that has a significant or heavy mass, often in a metaphorical sense.
Example: "The vast weight of his responsibilities began to take a toll on his mental health."
Alternatives: "Great burden" or "Heavy load."
"That is the vast weight under our relationship that keeps righting it when it tips".
Since the patient rights movement in the 1960's, legal scholars say, the vast weight of federal and state law has supported patient autonomy in medical decision making.
The lift of her legs over the gate reminded Rose of dockyards, cranes, and I-beams, vast weight swinging dangerously free.
He took the job, collected up the vast weight of Krays literature – including Reg Kray's Book of Slang, published from Parkhurst prison in 1989 – and decamped to London.
What is our answer to this vast weight of inertia and vested interest that keeps us all victims of the black evil?
Asia's stunning performance largely reflects the vast weight of China and India; most economies saw much slower growth, such as 4% in South Korea and Taiwan.
Mr. Tools lost vast amounts of weight and muscle mass during the months he suffered from heart failure and had a poor appetite and could not digest food properly.
It is less a traditional trade deal than a comprehensive economic treaty and, at least for the United States, a strategic hedge against the vast and growing weight of Chinese regional influence.
In an industry where actors routinely jeopardise their health by piling on or shedding vast amounts of weight, it's not much to ask someone to go to sleep each night with Learn German the Easy Way on their iPod.
Perhaps the most common suggestion is that he was suffering from severe stomach cramps, a result of him ballooning up in the size between the first and second bouts with Leonard and having to lose a vast amount of weight in a very short period.
Brody's immersion in roles is well-known – he lost vast amounts of weight for The Pianist (he was hardly chubby to start with), not to mention relinquishing his home and his relationship, he bulked up for Predators and took a part with virtually no words in M Night Shyamalan's The Village.
