How to make oil more heavy? I would like to increase the density of a given oil (or anything that repels water) so that it is slightly heavier than water; to be able to precisely control how slow the oil would fall in the water.

What can I add to the oil (or the water) to accurately set its density?

I am looking for a cheap solution, that I can easily do at home.

Edit

Another way to create slow and tiny drops would be to drop water into oil. Yet, the oil surface tension prevents water from falling down ; I asked another question for this problem.
Halogen-substituted aliphatic hydrocarbons are usually miscible with oils. Pick the compound by its density, price, safety, boiling point and other characteristics. 

For example, trichloroethylene (trico) has a density of ~1.6 g/cm3, and a Material Safety Data Sheet shows a vapor pressure of ~60mm Hg at room temperature and a time weighted average (TWA) toxicity limit of 50 ppm (269 mg/m3) from ACGIH and OSHA. Though it's readily available, trico might be too toxic and volatile for your use. A similar chemical is tetrachloroethylene, sold as "perc", with the same toxicity issue.

In general, going down the halogen group increases density, so bromine or iodine substituted compounds would be denser than those with fluorine or chlorine.