Definitely take some time time to sort/select your way through your flock looking for "table traits" to help the genetic side of how meaty they may get. That's all done through feel of the bird and getting hands on with the feel and structure. Going into dual purpose, I didn't know how varied it would be from bird to bird and breed to breed. Most of the breeds have not had hands-on selection breeding done for the table in quite a long while, with most lines becoming decidedly "egg bred"..
This picture shows a lot of structure differences, these birds are the same age at 18 weeks. American Bresse on the left and a Bielefelder on the right. Body length is about the same, but the width and depth are dramatically different, as well as the fleshing.
Diet does play a role in helping them gain, but the genetics need to be there too. I use a 20% all-flock for the duration of growth and may or may not do a special finishing with confinement. When I do the special finishing, I use 1/3rd cracked corn, 1/3rd whole wheat berries and 1/3rd of their regular feed. I make sure they have grit as well, to aid in digestion. I do that for a 4 week period, leading up to processing day.
This picture is one of my favorites. Same age at 16 weeks, same weight, different breed and different structure. Marans on the left after I spent several seasons on breeding selection for table traits. American Bresse on the right.
Once we got serious on breeding, I've found that I really only keep 10% of what we grow out. That's generally all that makes the cut after we account for as much as we can. It takes me about a year to get down to the best, since I account for rate of lay and egg size as well in the females. I don't want the flock to become "table bred" and lose their laying ability for the sake of size.
4lbs isn't a bad weight at all, depending on the age of the bird. There's more to what makes up the weight as well, such as meat to bone ratios. It's entirely possible to get a large framed bird with thick bones, that implies size, but then there's not much meat at all. Then on the flip side, if a bird has fine bone and a lot of meat, the table results would be dramatically different between that one and the larger boned one.
We've been dual purpose for almost 8 years now, there was a lot of trail and error in getting to where we are now with it. We ended up dropping down to just the American Bresse, so that I could use our pen space for them and breed them up better. Though I did recently add white Chantecler, to give them a try. The first trio are late bloomers and grow structure first, meat later. So I know that first season of chicks will need selected hard for early fleshing, so that I can fix that.
After we've gone through so many types and varieties that were touted as "dual purpose", the neglected traits always seemed to be body width, depth, fleshing and growth rate.