While I've never flown with Emirates, I've flown biz class with Austrian, Lufthansa, Air Canada, American, British, Qatar, South African and probably more airlines that I can't recall ATM and none of them measured my luggage. More than a few times I have been over (sometimes by more than 10lbs) the weight limit and other than 1 time with BA (who made me do some juggling between suitcases) I have never been charged a dime (though I'd be more than willing to pay).
Congrats on scoring Emirates biz class -- is it the A350? The bar/lounge on that plane looks very cool!