General Weakness:
* Weakness
* Delicacy
* Fragility
* Vulnerability
* Tenebrousness (literary, suggesting a fragile, easily broken state)
Moral Weakness:
* Flaw
* Fault
* Imperfection
* Vice
* Sin
* Infirmity
Physical Weakness:
* Debility
* Infirmity
* Ailment
* Illness
* Disease
Other:
* Ephemerality (short-livedness)
* Transitoriness (impermanence)
The best synonym will depend on the specific context and the meaning you want to convey.