Do most customers care about shipping weight? They care about shipping cost and delivery time, which may or may not be relative to weight. Might be more expensive to ship 10 pillows than 10lbs of chocolate.
I realize that they want to know and that wasn't really the point I was trying to make.
Given that the vast majority of shipping costs are related to weight (and dimension), most customers are looking at cost and delivery time since that's what they actually have a choice over (by choosing different shipping methods). They have no control over the weight other than choosing different quantities.
Providing them weight info might help them feel better about the cost of shipping (I.e. you're sending me a 50lb widget for $20, $40 or $80 depending on how fast I want it) but given they can't control it, it's just product feature info. But the product weight could certainly be provided as a product feature and shown that way with no modifications. Small hook could add the weight to the product detail page if so desired. Just have to determine your placement.
Darius provided a link to a free addon product from the marketplace.
We only ship flat rate so our customers are trying to cram as much as possible into that flat rate box. By displaying the weight, they won't be calling me asking me to calculate the weight to see if they have room for another product in the shipping carton. We have distributors that also need the total weight on their orders that are picked up by trucking companies. The add-on referenced is one of the first things I added because it will save me from so many phone calls.