Understanding and predicting how amino acid substitutions affect proteins is key to our basic understanding of protein function and evolution. Amino acid changes may affect protein function in a number of ways including direct perturbations of activity or indirect effects on protein folding and stability. We have analysed 6749 experimentally determined variant effects from multiplexed assays on abundance and activity in two proteins (NUDT15 and PTEN) to quantify these effects, and find that a third of the variants cause loss of function, and about half of loss-of-function variants also have low cellular abundance. We analyse the structural and mechanistic origins of loss of function, and use the experimental data to find residues important for enzymatic activity. We performed computational analyses of protein stability and evolutionary conservation and show how we may predict positions where variants cause loss of activity or abundance. In this way, our results link thermodynamic stability and evolutionary conservation to experimental studies of different properties of protein fitness landscapes.