Yes, the redesigned 2013 RAV4 is heavier despite being a little smaller outside and inside. See for yourself by using the Cars.com Compare feature, which lets you compare up to four specific models in detail. We set up a compare of the 2012 and 2013 here.
We didn't compare every version, but the 2013 base LE model with front-wheel drive weighs 3,435 pounds before any options are added. The comparable 2012 base RAV4 weighed 3,360 pounds. A 2013 Limited with all-wheel drive weighs in at 3,600 pounds, compared to 3,576 for a 2012 Limited with all-wheel drive. Overall length on the 2013 model is 179 inches, a couple of inches shorter than the 2012, and passenger volume has dropped to 101 cubic feet from 108.
Gas mileage is up despite the added weight as the 2013 RAV4 replaces a new four-speed automatic transmission with a new six-speed automatic. Front-wheel drive models go from 22/28/24 mpg city/highway/combined to 24/31/26 mpg, while all-wheel drive models go from 21/27/24 mpg to 22/29/25 mpg.
We only compared four-cylinder models because the 2012 also was available with a V-6, and the 2013 isn't. Stuffing the bigger engine under the hood raised the weight of a 2012 Limited with all-wheel drive to 3,699 pounds, so two more cylinders makes a difference on the scales.
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