We study the maximum weight independent sets of links between nodes distributed randomly in an infinite plane. Different definitions of the weight of a link are considered, leading to slight variations of what is essentially a spatial reuse problem in wireless multihop networks. A simple interference model is assumed with the interference radius equaling the transmission radius. In addition to unidirectional interference from a transmitter to the receivers of other links, also an RTS/CTS-type bidirectional handshake is considered. We study both the case where the transmission radius is fixed and tunable through power control. With a fixed transmission radius, we derive asymptotic results for the low- and high-density regimes. The main contribution is in the numerical results for the maximum weight, establishing some previously unknown parameters of stochastic geometry. The results are obtained by the Moving Window Algorithm that is able to find the maximum weight independent set in a strip of limited height but unlimited length. By studying the results as a function of the height of the strip, we are able to extrapolate to the infinite plane.