There is immediately a "bug" that i can think of; a 8-str wizard carrying a staff around. Is a staff heavy? Surely you can't cram 8 staves on your person. An 8-str character gets 0 heavy items allowed. Should 1 be allowed at a minimum?
Well, something that immediately sticks out to me is: why are you excluding the things you actually do carry around, literally in hand? That is, you're not counting the weight of worn armor, yet you are counting the weight of "wielded" weapons and shields. That seems strange to me! Why not count each piece of "equipped" gear as excluded? That gets around the "why can't a wizard lift his staff" problem without creating the "why can the wizard carry twelve staves without penalty" problem: the one staff actually "in hand" (or stowed, when needing both hands free) doesn't count, but any EXTRA weapons would.
To simplify issues of "multiple simultaneous-use items," e.g. sword-and-board or TWF, a character proficient in such stuff would consider sword-and-board (or two paired weapons) as a "single" heavy item, as long as they are kept together. If they are separated for some reason, they both count individually as heavy items unless properly paired again.
That way, a Paladin could swap from mace-and-shield to greatsword and not spontaneously "gain" an extra heavy item out of nowhere, nor "reduce" her load by switching back.