The phrase "weighty influence" is correct and can be used in written English.
You can use it to describe the power something has over a situation or person. For example, "His weighty influence on the board of directors was undeniable."
Yet it is also essential to gauge the extent to which men and women knew about these pressures and how far they interpreted them as 'burdens' that were sufficiently weighty to influence their behaviour.
His influence, although weighty in Arizona, clearly has its limits in actually propelling candidates to the White House.
But it offers a platform from which to exert real influence, mainly through weighty speeches.
As for the Reform Party, it now settles back under the spell of Mr. Perot, whose influence looks far less weighty with each presidential election.
Shermer considers the beliefs that motivate Intelligent Design's most prominent (and financially weighty) advocates and the problems with trying to influence science education through legislation rather than evidence.
To complicate matters, Paris now faces a weighty rival as China busies itself winning friends and influence on the continent.
Perhaps a strong economy has bred complacency, or perhaps the influence of the pollsters has grown even weightier.
Although his mode of thinking betrays a strong Aristotelian influence, it also displays a certain doctrinal affinity to Plato stripped of the weighty accretions of Neoplatonic interpretation.
But if the regional giant cannot influence events in this tiny country, it will struggle to project its interests in weightier places.
Lastly, although the Treaty of Nice will make enlargement of the EU a little easier, it is far from a done deal.Weighty mattersThe really bitter arguments in Nice were not about the principle of enlargement, but about the struggle for power and influence in a newly expanded European Union.
