At Popular Mechanics, an astute analysis based on "our keen analysis of the 2014 Godzilla toy and a formula developed by paleontologists to work out the mass of bipedal dinosaurs".
This summer Godzilla is back in theaters, and he's big. Since his first awakening, the radioactive, fire-spewing kaiju has grown 200 feet and put on more than 150,000 tons. Godzilla is now 30 stories tall and weighs as much as a cruise ship. No actual animal could take the pressure of being so massive: It would overheat, its organs would implode, and it would need to mainline butter to get enough calories. For fun, we surveyed scientists to help us break down the beast's biology.
The Popular Mechanics article includes more detail about his anatomy: Godzilla would weigh 164,000 tons, the force on his bones would be roughly 20 times greater than the force on a T. rex's, so his bones would need to be phenomenally strong—about twice as tough as some titanium alloys, and his crocodile-like hide would be embedded with osteoderms, or bony deposits akin to chain mail (with protruding osteoderms on his back and tail vent excess heat). Go there to read the whole thing.
Science! The Ever Increasing Size of Godzilla: Implications for Sexual Selection and Urine Production.