May just be the constant rain that causes it. 
The rain isn't constant in Angus. Eastern Scotland is in fact a relatively dry part of the country. Average annual rainfall at RAF Leuchars is 28 inches. This compares with 23 inches at Greenwich, 34 inches in sunny Blackpool, 42 inches at St Mawgan in Cornwall, 32 inches in Rome (Italy) and 51 inches in Orlando (Florida, USA).
It's the type of stone. Sandstone is relatively soft compared to granite, and therefore it was easier for the stonemason to carve in, and probably cheaper too.
Both Dumfries and Angus are in the Devonian sandstone, which is sand laid down about 400 million years ago and partly held together as stone by calcite. Calcite is the commonest form of limestone, and it dissolves in water, especially if the water is acid.
QED
The moral of the tale is, if you want your descendants to be able to find your headstone, get it done in granite. It won't last for ever, because even granite will eventually erode, but it will last a lot longer.