"heavily driven" is correct and usable in written English.
You could use it to refer to a situation in which something is strongly motivated by something else. For example, "The performance was heavily driven by the audience's enthusiasm."
The annual Oscar frenzy itself is heavily driven by New York.
However, he also admitted that the movie is heavily driven by myth and nostalgia.
"The ratings are heavily driven by how many goals there are.
"In today's environment," he said, "buyers of sports franchises need to see real value, which is heavily driven by media contracts.
When a bookstore's sales are heavily driven by the recommendations of a particular person — a Mary Gay Shipley — sleepers, relatively speaking, do better and blockbusters do worse.
This has been heavily driven by the growth of responsive web design, which is a great solution for building across both mobile and desktop.
The increase in quality, quantity, and complexity of recombinant products heavily drives the need to predictably engineer model and complex (mammalian) cell systems.
-- Reducing monetary stimulus will be heavily data driven.
The distribution of total dietary As intake and dose were heavily skewed, driven by the overwhelming contribution from contaminated drinking water for the upper 25th percentile of the population.
In interviews with police, former Ford staffers have made further accusations, saying the mayor drank heavily, sometimes drove while intoxicated and pressured a female staffer to engage in oral sex.
The expansion received critical praise for fixing various balance issues with the original game, development attention on par with that of a full game and for continuing with single player campaigns that were heavily story-driven.
