Why do some companies perform their freight flights only during the night?
As the previous answers have stated, their schedules are determined by what best suits their needs. However, those schedules can be complicated by contractual and curfew requirements.

A contractual example: Thousands of expatriate Brits live in the south of Spain. They want their morning London papers. We would depart Stansted (just north of London) as soon as possible. We were contractually committed to have the load to Barcelona by 07:00 local, with huge penalties if we failed (the papers were worthless by noon), and then on to Palma de Mallorca. Hopefully by now, they transmit the papers electronically and print them locally.

A curfew example: A cargo flight departing Hong Kong bound for Chitose, Japan (refuel there then on to Anchorage). The old Kai Tak airport at Hong Kong had a 23:00 local curfew; Chitose had a curfew until 06:00 local. The solution to that was to depart Hong Kong just before the curfew, land at Taipei and park for a couple of hours (I forget the exact time), and then continue to Chitose to arrive just after 06:00 local.

All Japan airports at the time had a curfew from 23:00 local to 06:00. You could go out to the south end of the airport just before 06:00 local, and set your watch by the first arrival of what was tens of aircraft, both passenger and cargo, whose departure time was determined by the need to arrive as soon as possible after the airport opened