40/40 sets

If I don't meet the requirement for the weapon do I get full/some/no benefit from the effect. If I get some effect what, exactly, is the percentage of benefit and does this vary with my attribute distribution in that attribute?

Req only determines whether or not you get the standard damage, armour or energy the item would otherwise normally provide. Everything else is not linked to attribute req.

Requirements on Staffs, Wands and Martial Weapons only affect their DAMAGE (if you don't meet it you deal much lower dmg), all other mods are fully functional even if you don't meet the req.
And in case of Focus items requirement only counts for the base +energy stat - if you don't meet the req you only get 6 base energy but all other mods are still fully effective. Same with shields and their base armor - if you don't meet req you get 8 armor (except some Nonmax crafter/collector/green shields where you get only 5), but still you get full benefit from all their other mods.

The requirement on items only affects the stat that precedes that requirement.

As others have said. req on effects the dmg on weapons ( 15-22dmg sword etc.) and the BASE energy on an offhand (+12). If you don't meet the req you just get half. 8 armor on shields (if 16) and +6energy on offhands (if 12). You will still get the 40/40 or the +15 energy -1 if you have that mod on.

8 armor on any shield if you don't meet the req (very very few special exceptions).

Effects that are not tied to a requirement are not mitigated if you do not meet the requirement.

Thanks guys.