Since we don't currently have quantity-based shipping, I think you'd need to do it like this:

1. Make all of your products have a weight of zero, except for those which will have shipping.

2. Enter a uniform weight for all of those products which will need shipping, e.g. 1 lbs or 1 kg.

3. Set up a rate which covers a weight range up to 6 lbs, so if they order a quantity up to 6 it will use the rate.

If someone orders more than 6, the weight will exceed what the rate covers so no shipping charge will be used.