The law of the iterated logarithm precisely refines the law of large numbers and plays a fundamental role in probability limit theory. The framework of sub-linear expectation spaces substantially extends the classical concept of probability spaces. In this study, we employ a methodology that differs from the traditional probabilistic approach to study the k-iterated logarithm law for weighted sums of stable random variables with the exponent α∈(0,2) within sub-linear expectation space, establishing a highly general form of the k-iterated logarithm law in this context. The obtained results include Chover’s law of the iterated logarithm, as well as the laws for partial sums and moving average processes, thereby extending many corresponding results obtained in classical probability spaces.