¿Qué significa "weddings that I attended more than one of I might add" - I don't either get why they need "of" here??? ?

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The "of" here is to connect the number "one" to the "weddings." People often say "I went to one of those..." or "I'll take one of these..."

In this case the word order is different. It could also be said like this:

"...weddings, of which I attended more than one..."

Regardless of the word order, the "of" is necessary to connect the quantity to the unit.

There is a case when the "of" can be dropped:

"...weddings, which I attended more than once..."

If you are counting general items ("I went to one wedding"), "of" is not necessary. If you are counting specific items ("I went to one of those weddings"), the "of" is necessary.