Considering a system comprised of two-level atoms resonantly interacting with weak coherent states trapped in two distant cavities connected by an optical fiber initially, we study the entanglement properties of the atom-atom, the cavity-cavity and the atom-cavity. Then the influences of the ratio between fiber-cavity and atom-cavity coupling intensity, the intensity and the phase of the cavity field on the entanglement properties are investigated numerically. It is shown that the entanglements of the atom-atom, the cavity-cavity and the atom-cavity vary with time in the periodical or approximately periodical manner; the entanglement can be transferred from cavity-cavity to atom-atom reciprocally. Compared with the entanglements of atom-atom and cavity-cavity, the varying period of atom-cavity entanglement is short. The ratio of fiber-cavity coupling intensity to atom-cavity coupling intensity and the phase of cavity field affect the entanglement properties greatly. The great entanglement can be achieved by using a smaller ratio of coupling intensity between fiber-cavity and atom-cavity.