Take It Off…Take It ALL Off!!
It looks good and it feels nice underfoot, but carpeting is one of the worst things you can do to a balcony. Carpet, artificial turf and similar floor coverings tend to hold water, impair drainage and retard evaporation. The longer water remains in contact with concrete, the more opportunity it has to exploit small cracks and the natural porosity of concrete in pursuit of a favorite target… steel (in this case the embedded reinforcement). When water contacts steel, it usually results in corrosion (rust). Rust occupies more space than the parent metal and the force that accompanies its formation is more than enough to shatter (spall) concrete that confines it.
If you simply cannot live without carpet on your balcony, at least coat the concrete with a protective surfacing; but beware, appropriate coatings are not cheap (and mere paint will not suffice). It should also be noted that carpeting will reduce the serviceable lives of coatings and fairly frequent re-application may be necessary.
It’s equally ill-advised to carpet wood balconies. Prolonged exposure to water contributes to decay (rot) and distortion (warping/cupping) of the wood, as well as corrosion of steel components.