'To heave in sight' definitions:

Definition of 'To heave in sight'

From: GCIDE

Heave \Heave\ (h[=e]v), v. i.
1. To be thrown up or raised; to rise upward, as a tower or mound. [1913 Webster]
And the huge columns heave into the sky. --Pope. [1913 Webster]
Where heaves the turf in many a moldering heap. --Gray. [1913 Webster]
The heaving sods of Bunker Hill. --E. Everett. [1913 Webster]
2. To rise and fall with alternate motions, as the lungs in heavy breathing, as waves in a heavy sea, as ships on the billows, as the earth when broken up by frost, etc.; to swell; to dilate; to expand; to distend; hence, to labor; to struggle. [1913 Webster]
Frequent for breath his panting bosom heaves. --Prior. [1913 Webster]
The heaving plain of ocean. --Byron. [1913 Webster]
3. To make an effort to raise, throw, or move anything; to strain to do something difficult. [1913 Webster]
The Church of England had struggled and heaved at a reformation ever since Wyclif's days. --Atterbury. [1913 Webster]
4. To make an effort to vomit; to retch; to vomit. [1913 Webster]
To heave at. (a) To make an effort at. (b) To attack, to oppose. [Obs.] --Fuller.
To heave in sight (as a ship at sea), to come in sight; to appear.
To heave up, to vomit. [Low] [1913 Webster]