"a great weight of" is correct and can be used in written English.
It is typically used to describe something that has a significant or heavy impact or influence. Example: The new policies put a great weight of responsibility on the shoulders of the employees.
A great weight of evidence puts that statement beyond doubt.
Switzerland had shouldered a great weight of history and the parallels had looked clear.
A sincere society places a great weight of emphasis on what we are really feeling.
Children of the Jacaranda Tree is a novel with a great weight of history attached to it.
Most social workers feel a great weight of responsibility, being only too aware of the long-term consequences for the child and everyone involved.
She is thrillingly solid, enormous, a great weight of limbs encased in stony drapery, her left hand pillowing her cheek, her right thrown back over her head.
Conversely, if the midships oarsmen row as hard as the others, they will move a greater weight of water and contribute more to the ship's movement.
In their fascinatingly louche and provocative way, they even teach the latter in primary schools; and their capital city, being so much more beautiful than London, carries a greater weight of melancholy and mystery.
Algorithms based on a proportion of records reporting a person as indigenous require a greater weight of evidence than the algorithm used in this study, and would result in a relatively smaller increase in the number of deaths reported as a result of the enhancement.
The optimization of PfRH5 vaccine formulations to achieve and maintain the highest possible levels of antibody will also be a major focus of human clinical trials that should commence within the coming year, supported by a greater weight of preclinical evidence than any previous blood-stage vaccine candidate.
For example, linkage could include records from health services that are dedicated to providing services to indigenous people, and these records could provide a greater weight of evidence that a person is indigenous than records collected as part of universal health services.
