This paper provides a general framework that accounts for the decay of the average contribution observed in most experiments on voluntary contributions to a public good. Each player balances her material utility loss from contributing with her psychological utility loss of deviating from her moral ideal. The novel and central idea of our model is that peoples moral motivation is "weak": their judgement about what is the right contribution to a public good can evolve in the course of interactions, depending partly on observed past contributions and partly on an intrinsic "moral ideal". Under the assumption of weakly morally motivated agents, average voluntary contributions can decline with repetition of the game. Our model also explains other regularities observed in experiments, in particular the phenomenon of over-contributions compared to the Nash prediction and the so-called restart effect, and it is compatible with the conditional cooperation hypothesis.