Certain weak type endpoint estimates are established for maximal commutators generated by $Calderacute{o}n-Zygmund$ operators and $Osc_{exp}L^{gamma}({mu})$ functions for ${gamma}{ge}1$ under the condition that the underlying measure only satisfies some growth condition, where the kernels of $Calderacute{o}n-Zygmund$ operators only satisfy the standard size condition and some $Hddot{o}rmander$ type regularity condition, and $Osc_{exp}L^{gamma}({mu})$ are the spaces of Orlicz type satisfying that $Osc_{exp}L^{gamma}({mu})$ = RBMO(${mu}$) if ${gamma}$ = 1 and $Osc_{exp}L^{gamma}({mu}){subset}RBMO({mu})$ if ${gamma}$ > 1.