What are the concerns and consequences of an overweight landing?
Two things:


Loads on the landing gear. This can be alleviated by carefully touching down, but you never know what exactly will happen in the next landing, so better don't count on it to be smooth
Deceleration distance: The higher mass requires a higher approach and touch down speed (higher by the square root of the mass ratio between your actual mass and the maximum certified landing mass). Now you have more mass and more speed, but the landing strip and the airliner's brakes are still the same. The risk is that you overshoot the runway with an airplane full of fuel or that you overheat the brakes (which will result in their failure, and again an overshoot). Since the kinetic energy is proportional to mass times speed squared, the energy which needs to be absorbed by the brake goes up with the square of the mass increase.


If the selected runway for your overweight landing is long enough and the weather is calm (so a smooth landing is easier), an overweight landing is not such a problem.

Now let's look at the 777-300ER in detail. I use the figures from Wikipedia, because the manufacturer's site is trying much harder to hide the relevant data. The MTOW (maximum take-off weight, which is actually a mass) is 351,534 kg, and the maximum landing weight is 251,290 kg, about 100 tons less. Now let's assume that taking off and returning to the airfield uses 5 tons of fuel, so the mass ratio is 1.379. Therefore, the approach speed has to be 17.4% higher and the total kinetic energy at touchdown is higher by a factor of 1.9 compared to the case at maximum allowable landing weight.

If we now assume that speed is reduced linearly during the landing run and that the wheel brakes will just absorb as much energy over time as in the case at maximum landing weight, the deceleration needs to be lower by the mass ratio, so the aircraft decelerates with only 72.5% of the deceleration at maximum landing weight. To shed its kinetic energy, the landing run will take longer by the increase in kinetic energy, i.e. 1.9. Since the average speed is also higher by 17.4%, the landing distance will be higher by a factor of 2.233 or 223% of the landing distance at maximum landing weight.

This neglects that the heating of the brakes is an instationary process, so you cannot simply brake with the same intensity for more than twice the time they were designed for. But this little estimation should illuminate what impact a higher landing mass has on the energy and distance involved.