Sometimes new growth starts out smaller and then gets larger as it ages, other times it can be a sign that the grafted rosebushes root stock is pushing up canes. Grafted roses have the part that we buy them for above ground while their root stock is an entirely different rose that is very hardy. The grafting is done to make for a hardy rose that can survive in most any climatic conditions. Sometimes the root stock gets a bit over zealous and pushes up its own canes. This robs the top part of the grafted rose that we desired of nutrients and strength and will eventually lead to its death. In such a case i highly recommend pruning out those canes with the different look all the way down into the ground, as close to the graft as possible. Seal the cut area with Elmer's white all purpose glue or the Tacky Glue you can get at craft stores.
