The phrase "a considerable weight" is correct and usable in written English.
It can be used when discussing the significance or impact of something, often in a metaphorical sense, such as emotional or intellectual weight.
Example: "The decision carried a considerable weight, influencing the future of the entire organization."
Alternatives: "a significant burden" or "a substantial impact".
A considerable weight had been lifted.
That said, he's labouring under a considerable weight of expectation.
Even though they seem insubstantial they carry a considerable weight of water – around 500 tonnes in a small cumulus cloud.
21-year-old Melissa Hamilton has been used extensively by McGregor, and a considerable weight of expectation rests on her slender shoulders.
He has been given a lot – funding, dancers, a company residence in Brighton – and with all of this comes a considerable weight of expectation.
Barcelona play their second leg first and Real will be carrying a considerable weight of expectation should they come to White Hart Lane next month needing a result to set up a Clasico.
Dinkins, Mr. Koch, the incumbent, endorsed him — an endorsement that carried considerable weight in a race against a popular prosecutor (Mr. Giuliani) who was challenging a candidate who needed every white vote he could win to be elected the city's first black mayor.
Even with a human islet graft, Rag2 /– mice on a HFD gained considerable weight (Fig. 1a) as compared with mice on the control diet (p < 0.0001).
Six patients (11.3%) had a history of considerable weight loss and 12 patients (22.7%) reported an increase in weight during the last year.
Officials with the Parliamentary Assembly of the Council of Europe, a group with considerable weight in assessing progress toward democracy of former Eastern bloc countries, issued a darkly worded warning to the Georgian government at a news conference.
"How deeply, beyond words, he speaks to us," he said--a phrase that, coming from a great writer, carried considerable weight.
