Have seen a video of the Su-34 launching a Yakhont, which is 2.5 tons... and that is as heavy as any model of Club.
The Moskit was also designed to be centreline carried and launched from Flanker sized aircraft and it was 4.5 tons in the air launched version.
The Club-K is the mockup posted above and is intended to be carried by Su-35.
The Club, or Klub family includes 5 different missiles and they are the:
3M-54E - Anti-shipping variant, Basic length 8.22 m, with a 200 kg warhead. Range is 200 km. Sea-skimmer with supersonic terminal speed and flight altitude of 15 feet (4.6 m) at final stage(2.9 mach).
3M-54E1 - Anti-shipping variant, Basic length 6.2 m, with a 400 kg warhead. Range is 300 km. Sea-skimmer with subsonic terminal speed(0.8 mach). Allegedly capable of disabling or even sinking an aircraft carrier.
3M-14E - Inertial guidance land attack variant. Basic length 6.2 m, with a 400 kg warhead. Range is 275 km. Subsonic terminal speed(0.8 mach).
91RE1 - Submarine launched anti-submarine variant, with an anti-submarine torpedo. Basic length 8.0 m, with a range of 50 km. Supersonic speed. The torpedo has a warhead weight of 76 kg. This, along with the 91RE2, are similar to the American ASROC/SUBROC missile/torpedo system. Follows a ballistic path into the surface, speed is 2.5 mach.
91RE2 - Ballistically launched anti-submarine variant, with an anti-submarine torpedo. Basic length 6.5 m, with a range of 40 km Supersonic speed. The torpedo has a warhead weight of 76 kg. For surface ship use only. The lightest of all variants, with a launch weight of 1300 kg. Speed is 2 mach.
The mockup in my previous post shows the 3M-54AE positioned below a poster of a Su-35, which is a member of the Klub or Club family, as is the 3M14AE in front of the Mig-29SMT.
The 3M14AE in many ways is just a Harpoon with a much heavier warhead.