Step 1: What the statement is asking:
A conventional weapon means guns, swords, cannons and armies. The statement says the Spanish did not win mainly by these. We must give two reasons to prove it.
Step 2: First reason: diseases moved faster than armies:
Smallpox and other Old World diseases reached the Americas along with the Europeans. They passed from person to person and travelled deep into the land, much before any European soldier did.
People were dying of the disease even in places the conquerors had not yet visited.
Step 3: Second reason: the native people were defenceless:
America had been isolated from Europe and Asia for a very long time. Its people had never met these diseases, so they had no immunity.
When an epidemic came, it killed huge numbers and wiped out entire communities. A weakened society could not resist the invaders.
Step 4: Round off the argument:
In this way, a silent biological weapon helped Spain take over the continent in the sixteenth century, and that is why the statement is correct.
Final Answer:
Germs and the lack of immunity in native Americans were the two reasons that made disease the Spanish conqueror's most powerful weapon.
\[\boxed{\text{Disease was the most powerful weapon}}\]