Any Geoligests here

.one geology method to identify basalt

Get a piece of unglazed tile, scratch it hard with the rock.
If it leaves a brownish streak it could indicate the presence of iron rich minerals, the brown streak could be
Oxidizing iron (rust) particles
The OP said that it was not magnetic.
There still could be particles of iron in it, but not enough to be "feel" magnetic
Iron could explain the "heaviness"
(Density) of the rock.

Limestone was mentioned
Place a few drops of dilute hydrochloric acid on the rock, if it sizzles or bubbles it will more than likely be limestone, from ancient sea shells, which are composed of calcium carbonate.