A high level Vault with poor weapons will not weather the damage.

This is because as the levels of the dwellers increase, enemies will attack more frequently and become steadily more powerful. It's generally a good idea to stock up on weapons and steadily upgrade all Vault Dwellers' equipment as new types become available. Weapons can be stored in the storage room. Weapons can be brought by dwellers sent to explore the Wasteland, obtained through cards found in lunchboxes, and occasionally Rare or Legendary Dwellers may come equipped with their own weapon. The damage is determined entirely by the sum damage of weapons wielded by dwellers and determines how fast the enemy health bar is depleted.

Note that the animations have no bearing on damage being dealt. They are used to equip Vault dwellers who are unarmed by default, and are useful for protecting your Vault against attacking raiders and creature infestations, as well as improving the chance that explorers survive. There are a variety of weapons featured in Fallout Shelter.

Fallout shelter weapons list