We have studied the optical properties of a hybrid system consisting of cyanine dye J-aggregates (both PIC and TDBC) attached to a spherical microcavity. Instead of the commonly accepted chemical bonding of dye molecules to the surface of microspheres or deposition of dye-doped sol-gel film, in our experiments microspheres were coated with J-aggregate shell utilizing the layer-by-layer assembly of the ultrathin films. In this approach we aimed to take advantage of light confinement in the Whispering Gallery Modes (WGMs) microcavity by placing the emitter (shell of J-aggregates) just at the rim of the microsphere, where the resonant electromagnetic field reaches its maximum. A periodic structure of narrow peaks was observed in the photoluminescence spectrum of the J-aggregates, arising from the coupling between the emission of J-aggregates and the WGMs of the microcavity. The most striking result of our study is the observation of polarization sensitive mode damping caused by re-absorption of J-aggregate emission. This effect manifests itself in dominating emission from the transverse magnetic modes in the spectral region of J-aggregates absorption band where the transverse electric (TE) modes are strongly suppressed. Strong suppression of TE modes reflects preferential tangential orientation of transition dipole moment of J-aggregates in deposited microcavity shell. Observed polarization sensitive mode damping observed in the spectral region of high J-aggregate absorption can be used for suppression of unwanted modes in high Q optical resonators. We also demonstrate that the emission intensity can be further enhanced by depositing a hybrid layer of J-aggregates and Ag nanoparticles onto the spherical microcavity. Owing to the concerted action of WGMs and plasmonic hot spots in the Ag aggregates, we observe strongly enhanced Raman signal from the Jaggregates. Microcavities covered by J-aggregates and plasmonic nanoparticles could be thus useful for a variety of photonic applications in basic science and technology.