The best replacement for burden is overhead.

The best alternatives to burden are rated as following:
★★★★★  overhead
★★★★★  responsibility
★★★★  benefit
★★  burden
★  white mans burden
★  shelter
★  fringe
  labor

Your alternative for burden is not listed? Suggest!
Speaking about burden, one probably shouldn't forget about load.

Other search terms related to burden and their ratings are:
★★★★★ load
You have in mind a companion for burden and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of burden in all years. Click on graph for more.
burden
overhead
responsibility