"weighty authority" is correct and usable in written English.
You can use this phrase to refer to a person or source that is respected and has a lot of influence. For example, "The mayor's opinion on the matter was given weighty authority due to his decades of experience in the field."
For me, notwithstanding some of the weighty authorities mentioned above, it was entirely right that Britain entered the war.
The Sunday Times noted: "What makes this book worthwhile is its fiercely illuminating angle.... Morrison, as usual, declined to take part but the author's scholarly methods lend this weighty volume a real authority".
Even as the Metropolitan Transportation Authority seeks to overcome a $1.2 billon shortfall with fare increases and service cuts, an even weightier problem looms: The authority is uncertain how it will pay for a five-year capital spending plan that could cost as much as $30 billion.
It is simply unfair to victims, and to the accused military members that a convening authority makes these weighty calls based on a few hours of training.
But the share of the vote garnered by each party, and the number of votes a party wins compared with the number of seats, might lend a moral authority that is weightier than the sheer arithmetic allows.
Franklin's weighty words will be lent a special authority by the voice of Walter Cronkite.
The alcohol-debilitated household, with Nanny, a sternly penny-pinching grandmother, and Louise, an increasingly embittered mother perpetually battling for the love of and authority over the young girl, feels like a weighty burden for her to have overcome.
Mthunzi Mhaga, a spokesman for the national prosecuting authority, said the charges against the journalist were more weighty than against the fan.
