"largely outweigh" is correct and usable in written English.
You can use it when you want to denote that one thing is much more important or beneficial than another. For example: The cost savings of using a computerized system largely outweigh the initial investment.
But for Putin the political gains of harnessing an ally, demonstrating steadfastness and parading Russian clout in the Middle East – while the west wallows in confusion – largely outweigh that apparent contradiction.
As long as diseases such as cancer and dementia remain primarily diseases of the elderly, the benefits of nuclear and X-ray imaging will largely outweigh the risks.
But we can realize that the benefits for our children can largely outweigh any concerns we might have.
Did she realize that the benefits for her child would largely outweigh any concerns she might have had?
It found the benefits of the $15.25 wage increase — improving the living standards of low-wage workers — would largely outweigh the costs.
While broken bones, knee injuries and concussions rise to the top of the fear factor list, the overall perceived benefits seem to largely outweigh the risks for parents of youth involved in sports.
But the positives at the Apthorp largely outweighed the negatives.
"But that benefit is largely outweighed by the bad because, once again, we've seen doubts cast over the way that carbon markets are working".
But all that is largely outweighed by another factor: health campaigners say that in many countries booze is simply too cheap.Increasingly alcohol is drunk at home, rather than in bars or restaurants, and is often deeply discounted.
Although there could be significant disadvantages associated with AVs, it is widely believed that these disadvantages are largely outweighed by the advantages.
However, previous results in borides indicate that the penalty from reduction in electrical conductivity with porosity typically largely outweighs the benefit in reduction in thermal conductivity [30, 32, 39].
