A fiber structure for reinforcing a composite material part, the structure being woven as a single piece by multilayer weaving between a first plurality of layers of yarns extending in a first direction and a second plurality of layers of yarns extending in a second direction. The second plurality of layers of yarns includes at least one layer of variable-weight yarns, each variable-weight yarn including a separable assembly of individual yarns, each having a determined weight. The fiber structure includes at least one portion of reduced thickness in which the variable-weight yarn presents a weight that is less than the weight that it presents prior to the reduced thickness portion.