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Abstract: We prove that the twistor lifts of certain twistor holomorphic surfaces in four-dimensional manifolds are weakly stable harmonic sections. As a corollary, if ambient spaces are self-dual Einstein manifolds with nonnegative scalar curvature, then the twistor lifts of twistor holomorphic surfaces are weakly stable. Moreover, for certain surfaces in four-dimensional hyperkähler manifolds, we show that the surfaces are twistor holomorphic if their twistor lifts are weakly stable harmonic sections. In particular, we characterize twistor holomorphic surfaces in four-dimensional Euclidean space by weak stability of the twistor lifts. [Copyright &y& Elsevier]