What are the weapon ranges?

9 tiles, put simply.

9 tiles straight is the range at which most weapons' aim changes. 6 diagonal, if I'm reading this Google Sheet correctly.

• Shotguns get a proportional bonus if less than that distance. Proportional penalty if greater than that distance. Ranging from +52% to -40%.
• Sniper rifles get a proportional penalty if less than that distance (up to -24%).
• Rifles, LMGS, and pistols get a proportional bonus if less than that distance (up to +37%).

https://www.ufopaedia.org/index.php/Chance_to_Hit_(EU2012)#Weapon_Range

The Arc Thrower has a maximum range of 3 tiles. Its odds of success are 49/70/80/90% at 4/3/2/1 enemy HP respectively.