Increasing blade chord can give more lift, but only up to a point. Helicopter blades are pushing a column of air downwards, accelerating it from stationary to whatever speed is necessary. Each time a blade passes the same point, it gives that part of the column a push downwards. If the air hasn't really slowed down from the previous blade, then the blade adds nothing useful. So there's a limit to how much air each blade can push before it interferes with the next blade - and pushing a fat blade around causes drag and requires power, even if it's not doing anything useful.
For maximum efficiency, you want long, narrow, slow moving blades, so that each one is in 'clean' air.