(Cessna 185 Skywagon and Cessna 340)
See here for the major points: What are the pros and cons of single-engine vs. twin-engine? Regarding your specific question:
Wouldn’t a single engine plane weigh less and thus can fly longer on a specific amount of fuel comparative to a twin engine plane?
Both airplanes above are powered by the same 300 hp engine, so yes the twin will be heavier. But it can also lift more weight (i.e. more fuel), and cruise at a higher speed for the same power setting, or cruise at the same speed for lower power setting.
Either the higher speed or lower power, combined with the more fuel, gives the twin a longer range.
In fact, double. 2,603 km compared to 1,333 km.
If you wanted to compare the twin to a single with a 600 hp engine, then there is no weight advantage. Only the bigger engine is harder to maintain.
On a technical note, weight is not a big issue in cruise. The power to overcome the induced drag from the lift (which counters the weight), decreases with speed, i.e., it takes less power to create lift in cruise, than at slow speeds. (See graph below for the induced drag.)
Twins are designed to fly on one engine, which means half the power potential is enough, which is helped by the bigger span wing. So the same fuel load will give the same or more range for the twin. Unless, you want 600 hp vs 2x300 hp, in that case the single will win because of its smaller form.
For the two planes above, here are the gallons-per-hour and cruise speeds:
gph cruise speed kts
Twin 26.0-34.0 202-229
Single 11.7-15.5 122-140
As you can see, the higher fuel consumption is offset nicely by the speed, and note that the twin will reach the cruise altitude in less time as well.
Sources: Cessna 185, Cessna 340
If we compare a twin-piston to a single-turbine then it won't be an apples-to-apples comparison, but the single-turbine plane will be faster, and will have longer range, but that's mainly due to the different engine types (combined with different cruise speeds). For the Cessna Caravan, the turboprop engine (minus the accessories) weighs as half as a single 300 hp piston engine, which can allow for 200-400 kg more fuel, but the turboprop engines are very, very expensive. So depending on the operation, a fuel saving here might be overdone by the initial cost.