What prevents a malicious user creating a new transaction using signatures of an old mined transaction if the inputs have the exact same balance?
The transaction ID and output index of the second 1 BTC that was sent to A's address will be different from the first 1 BTC that was sent there. Since transactions refer to inputs by their txid and output index, the signature used in the first transaction will not be valid for another tx trying to spend the second deposit.

Additionally, depending on the type of Signature, it may also restrict that the output can only go to B's address.