Sort of. Full-frame mirrorless bodies are most definitely smaller and lighter than their DSLR counterparts. The problem is the lenses, and those are a problem for two reasons.
One is that many manufacturers haven't taken advantage of how mirrorless changes lens design yet (the shorter flange distance enables a lot of design space), so you're still carrying a lens designed for a DSLR, but with a lot of hollow space between the back element and the mount. This is especially obvious with third-party lenses; e.g. it's well understood that a lot of Sigma lenses for Sony FE are functionally just their DSLR lenses with a built-in adapter.
The other reason why you don't see a big weight advantage with mirrorless lenses is that, where they are designed for mirrorless specifically, they tend to aim for "better" rather than "lighter. Lenses like the Canon 85mm f/1.2, the 50mm f/1.2, and the 28-70 f/2.0 are perfect examples of this.
However, lenses designed to take advantage of mirrorless can be smaller and lighter, when they have the same design goals — e.g. the latest (DSRL) Canon EF 24-105L f/4 weighs 795g vs the (Mirrorless) RF 24-105L f/4's 694g.
One is that many manufacturers haven't taken advantage of how mirrorless changes lens design yet (the shorter flange distance enables a lot of design space), so you're still carrying a lens designed for a DSLR, but with a lot of hollow space between the back element and the mount. This is especially obvious with third-party lenses; e.g. it's well understood that a lot of Sigma lenses for Sony FE are functionally just their DSLR lenses with a built-in adapter.
The other reason why you don't see a big weight advantage with mirrorless lenses is that, where they are designed for mirrorless specifically, they tend to aim for "better" rather than "lighter. Lenses like the Canon 85mm f/1.2, the 50mm f/1.2, and the 28-70 f/2.0 are perfect examples of this.
However, lenses designed to take advantage of mirrorless can be smaller and lighter, when they have the same design goals — e.g. the latest (DSRL) Canon EF 24-105L f/4 weighs 795g vs the (Mirrorless) RF 24-105L f/4's 694g.