Heavy rocks afloat - Ram Setu Bridge, Rameswaram Island, SE India

Floating rock pieceRameswaram.vaishnava.in

A natural stone bridge, interwoven with the Hindu mythology - the Ram Setu Bridge – also known as Adam's bridge is a long string of coral reef rocks that connects the Rameswaram Island in Tamil Nadu, India to Mannar Island, off the north-western coast of Sri Lanka. This bridge is believed to have been built across the sea for the Hindu God Sri Rama by Hanuman and his associates when they marched across a small strip of sea to Lanka to fight King  Ravenna and bring back Seetha (Sri Rama's wife) who was in siege. In the Sanskrit epic Ramayana, it is mentioned that they jerrybuilt a passable stone bridge across the sea to cross over to the island country.

These big fragments of reef rocks were exposed after the worst devastating Tsunami that struck the eastern coast of India and other places on December, 2004. These huge coral reef rocks actually float in the water and never get submerged because of lots of void spaces in them. It may be possible for humans to use these series of floating stones and cross a huge water body.

At Rameswaram I myself saw in some places huge stones weighing more than 15 kg floating in big water tanks without getting submerged. After observation first hand logical explanation is - invariably almost all the floating stones are coral reef rocks made of calcium carbonate. They have lots of very small hollow spaces once occupied by colonies of tiny animals that normally build the reef in the coastal marine waters; most reefs were built by stony corals eons ago. Some newspaper articles report that such rocks are volcanic rocks and the floating rocks could be pumice.  As far as Rameswaram and adjacent areas  are concerned there are no  outcrops of Volcanic rocks. Nor are there occurrence of Pumice. Pumice is of volcanic origin.   Floating coral reef rocks are  lightweight with skeletal remains of coral organisms or porous limestones that have become trapped with air, due to sliding  in the continental shelf area.  Further coral reef formations occur in the tropical areas in the inner and middle continental  shelf. shelf.   coral reef is an important part of an underwater ecosystem characterized by reef-building corals. Reefs are formed of colonies of coral polyps held together by calcium carbonate. 

Volcanic pumice en.wikipedia.org

Pumice  is formed when superheated when  highly pressurized rock is rapidly ejected from a volcano. The unusual foamy appearance  of pumice is due simultaneous rapid cooling and depressurization,  the latter creates bubbles by lowering the solubility of gases (including water and CO2) that are dissolved in the lava. This is akin to opening the carbonated water bottle, causing the gases to rapidly exsolve.

The numerous small air cavities in the rocks are not even and are found to occur unevenly inside them and also on the surface. Further, the weight of the water displaced by them is more than their own weight. As for buoyancy, the following inference can be made: Almost all floating stones at Rameswaram are coral reef rocks with variable density and air cavities.
The floating rock segment exposed to the viewer above the surface has more air cavities and less density. On the other hand, the bottom segment (immersed in water) has more density and less air cavities. Further, it is likely, it may be due to salinity of the floating medium - water.
No matter how you drop the stone into the water, it automatically realigns itself in such a way that less denser portion with more air cavities is turned towards the viewer.