Several methods exist for electing committees of representatives and conducting multiple referenda based on approval voting. Recently, a family of rules for approval-based voting using ordered weighted averaging was proposed, ranging from a simple candidate-wise majority (minisum) to egalitarian rule (minimax). Even though the first rule is strategyproof and the second is not, due to its egalitarian nature, only a partial study on manipulation has been conducted for inbetween rules. This paper investigates the manipulability of fair rules within this family. We first prove that all rules parameterized by fair (non-increasing) weight vectors are manipulable, except minisum, if we consider them either resolute with a tie-breaking mechanism or irresolute with classic extension principles. Then, we conduct an empirical study of the proportion of elections that are manipulable, showing that it increases based on the rule's fairness.