The object will weigh relatively the same regardless of the substance the object is in. It will "weigh" the exact same if it is in the water vs. if it is in the air.

The difference is how much downward force it would place on the item holding it. The water resistance pushing upwards makes the rock feel "lighter" in water, and makes it easier to move, vs virtually no air resistance supporting you.

You could encase the rock in cement and it will still weigh the same, it has nothing to do with the density of the water, etc.

There would be minor fluctuations based on the amount of water surrounding the rock, and the altitude of the rock.

If you are talking where someone holding onto the rope would feel the rock was the heaviest, you get into all sorts of variables, since as the person lowers the rope, they will have the weight of the rock, plus an ever increasing mass of rope. (1000m of rope gets heavy).

Assuming for purposes of arguement that the weight of the rope was either constant or ignored, the contribution of downward force the rock would have would be greatest at the air level, drastically reduced by placing it in the water, and somewhat reduced as it is lowered, as someone pointed out, the density of the water increases.

However, as I pointed out earlier, you'd have to lower it a long way for the density to become a factor, at which point you'd not only be holding up a rock, but a long length of rope as well.