Architectural heritage is deeply threatened by extreme weather events due to ongoing climatic change. Since these phenomena are becoming more and more serious, their effects cannot be neglected when a reliable assessment of a historic masonry structure is required. In this paper, the phenomenon of rising damp was studied, focusing on the influence of water on the unit weight of masonry walls made from fired clay bricks and lime mortar. This study consists of a basic experimental research on the variations in the unit weight of masonry undergoing an ageing treatment, which was simulated through some cycles of capillary water absorption and temperature changes. The experimental study proves that penetrating damp causes an increase in masonry unit weight of more than 20%. This basic result is significant in the structural assessment of historic masonry buildings. Subsequent papers will analyze the interaction with strengths parameters.