"heavy risk" is a perfectly valid and usable phrase in written English.
You could use it when making a comparison between two or more risks. For example, "Investing in international stocks carries a heavy risk compared to investing in domestic stocks."
Wise as that seems, the alternative proposal carries heavy risk.
An operation to remove it would carry a heavy risk of paralysis.
ING said: Antisoma shares are, we believe, significantly undervalued despite our heavy risk adjustments on ASA404 and the company's other phase III candidate, [blood cancer treatment] AS1413.
It would reduce the overall debt burden on Greece's economy, but would also create the heavy risk of pushing spooked investors to deny Greece access to credit markets.
For most of the countries involved, this desire to consult the people about European integration is new, and itself reflects growing uneasiness about the popularity of the European project.The constitutional referendums will carry a heavy risk for the EU.
If a country fell out of compliance, the fiscal authority it would be penalised it by restricting the amount of eurobonds it would be allowed to issue; it would have to borrow the balance in its own name and pay heavy risk premiums.
It carries heavy risks, of which the Administration seems well aware.
Details of the programme, which came laden with heavy risks, were pieced together by the Associated Press following interviews with numerous current and former US officials who were familiar with it.
Housing is not the only area of heavy risk-taking.
In other words, the in principle avoidable consequences of a policy of depletion (IPCC 2014, 10 17) impose heavy risks on future people by significantly increasing the likelihood of very many future people's basic human rights being violated (see, e.g., Caney, 2010).
Despite the heavy risks, the post-storm employment prospects were, to many impoverished workers, a welcome uptick in labor demand.
