Yup. The camera body may be lighter, but sensor format can also play a huge factor in the size/weight of things. And regardless of whether a lens is made for mirrorless or full frame, unless you're moving to a pancake lens design for a walkaround prime or kit lens zoom, the chances are really good an equivalent lens with the same max. aperture is going to be
more or less the same size/weight.
That doesn't mean you can't save on bulk, but only if you stay at the same sensor format or go smaller. A lot of the myth that mirrorless means less weight/bulk than dSLR came from the fact that initially, when mirrorless first came out. a lot of folks were moving from full-frame dSLRs to micro four-thirds