Of course, we all know about hindsight, but I believe there were several reasons Washington did not fire on the ships.
First of all, I’m pretty sure Washington received a “gentlemen’s” letter from Howe who said he (Howe) planned to withdraw (after realizing Washington’s new position, of course). Now, if Washington agreed to allow him safe passage, which he may well have, then that would have been that.
Also, the weather was terrible – severe wind and rain – and that would have effectively shut-down both armies in those days.
On top of that, I’m sure Washington believed that the British might still try to take the heights. And as his powder and ammunition was severely limited – remember, he had some major logistics problems in March 1776 – he felt the need to conserve enough to both repel a fresh landing and defend his position.