[lhnz]

"Strong opinions, weakly held" sounds right to me.

I couldn't care less how confidently somebody holds an opinion.

I think the word "strength" here should signify a battle-hardened opinion that has won out over others in a practical or theoretical sense. Strongly-supported...?

That's not to say that that it's wrong to be confident in the opinions you hold, but if you want to have strongly-supported opinions you can't protect them from being tested against other opinions. Let them win on their own merit...