How can the density of water be maximised?
Clerici solution is a solution of equal parts of thallium formate and thallium malonate in water, density is 4.25 g/ml,     Thoulets solution is solution of potassium-mercury iodide in water with density 3.2 g/ml. Don't even think of using them. 

Sodium polytungstate $\ce{Na6[H2W12O40]}$ is a relatively safe compound and allows densities up to 3.1 g/ml. $\ce{ZnCl2}$ allows densities up to ~ 1.9 g/ml, but has acidic solutions. 

Unfortunately, common nontoxic salts usually either are not dense enough or not soluble enough to make really heavy liquids, but densities around 1.1-1.2 g/ml are quite easy to achieve even with common salt. Note, however, that concentrated salt solutions 'siphons' water from human body through damaged skin and mucous membranes, and to some extent even through undamaged skin, which may lead to desiccation, trauma of mucous membranes and very unpleasant sensations.