Personally it depends what your aim is.
If you are building a dedicated track car then skinnies should reduce rolling resistance and weigh less. But on a stock or near stock vehicle I personally feel the difference they are likely to make would be minimal at best.
The down sides are IMO skinnies often make cars look fairly stupid and loose the stance they had. Also on road performance (i.e. cornering) will be massivly compromised.
I guess a cheap option could be to weigh a space saver spare wheel compared to a stock wheel and see if they are lighter. And use these as a budget alternative.