We study the response of the surface stress to excess charge via ab initio simulation of metal surfaces in an external electric field. We focus on "simple" sp-bonded metals to gain insight into the mechanisms underlying electrocapillary coupling. Both the direct effect on the surface stress via charging of the bonds and the indirect effect resulting from the charge-induced relaxation are analyzed and discussed in relation to the trends of the coupling coefficients, which-owing to a Maxwell relation-are determined in terms of the response of the work function to strain. Al(111), Mg(0001), and Na(110) are investigated as prototypical sp-bonded metal surfaces with positive, vanishing, and negative coupling parameters, respectively. Mg(0001) and Al(111) exhibit an inward relaxation of the first atomic layer upon negative charging, whereas an outward relaxation occurs for Na(110). The indirect contribution of the relaxation to the coupling coefficient has the same sign as the total response and makes up about 30% of its magnitude for Al(111) and Na(110). Our study highlights that even the response behavior of the so-called simple metals is by no means readily captured within simple models.