When you spend the transaction/sign a message, you are giving out the public key only, together with the public key. The signatures are signed using ECDSA. As of now, the repeated signing of a signature using the private key does not weaken the address by any extent. However, it would be a different story if your client is flawed. If your client generates the same "K" value for each signature, it is possible to derive the private key using the public key. If quantum computing were to be more advanced, it can potentially break ECDSA.
I've had addresses which were used for more than 3 years, with 700+ transactions and nothing happened. I trust ECDSA to be safe enough, at least for now. The only concerns regarding address reuse is privacy.
Thanks!