"weigh the possibility" is a correct and usable phrase in written English.
It means to consider or evaluate the likelihood of something happening. Example: Before making a decision, it is important to carefully weigh the possibility of unforeseen consequences.
The F.B.I., he said, needed to weigh the possibility that post office sorting machinery might have had an effect.
Instead, both forwarded the evidence to Congress so that the House of Representatives could weigh the possibility of impeachment.
How do we weigh the possibility that strikes against ISIS might help the regime of Bashar al-Assad or enmesh us in his war?
Just before a United Nations Security Council delegation arrived here to weigh the possibility of sending 5,500 peacekeepers to Congo, violence erupted in another corner of Africa.
For example, they weigh the possibility of introducing a me-too product if a rival comes out with a new offering.
Against concerns that the pace of growth remains subpar, the Fed continues to weigh the possibility that its efforts will destabilize financial markets by encouraging excessive risk-taking.
All that leaders can do is weigh the possibilities as best they can and find a way forward.
"One has to weigh the possibilities, avoid acting mechanically and, instead, act with a clear understanding of the situation," he said.
Democratic members of the committee were weighing the possibility of handing the gavel to another senior member, possibly Representative Sander M. Levin of Michigan, or even naming co-chairmen.
Portugal, France and Ireland have also committed to taking prisoners and several other European countries are weighing the possibility.
Entergy promptly installed new managers and weighed the possibility of shutting the troubled plant for repairs.
