Excessive bail shall not be required, nor excessive fines imposed, nor cruel and unusual punishments inflicted.
As I learned during Jerry Agar's "Drive-By Education" series on the Bill of Rights with guest, Constitutional attorney John Armor, a fine is not the same as a punitive damage award. A fine is imposed by the state, to be paid to the state. Punitive damages or other judgements in civil court, are paid by the defendant to the plaintiff (the injured party), not the state. It has always been understood that these Amendments regarding trials and searches and stuff apply to criminal cases, not civil cases. A Civil trial involves a plaintiff and a defendant. Criminal trials are the state vs. the defendant. For instance, the Fifth Amendment protection against self-incrimination doesn't apply in a civil trial.
Except that a fine is fundamentally different than a punitive damages award. A fine's amount is mandated by statute, often with some judicial discretion allowed. A punitive damages award depends on the case, and is frequently set by a jury.