Thickness: graphene is only one layer. There are people who use the term "multi-layer graphene" for thin stacks, but that already shows deviations in the behaviour from actual single-layer graphene.
Bandgap: actual, ideal graphene has "Dirac cones" at which the conduction and the valence band touch, so it does not have a bandgap. A bandgap results only from its rim termination and is, in the case of ribbons, dependent on the width, or, in the case of nanographene / graphene quantum dots, dependent on the dot area. The stack thickness has a negligible influence on that.
Electron affinity: is also dependent on the ribbon or dot dimensions.