There are two issues for me: weight and time. Chlorine Dioxide is my chemical of choice, be it Aqua Mira or MicroPur tablets. I use Aqua Mira as the first choice, with MicroPur tablets in my survival kit and taped to the bladder in my day hiking hydration pack.
The only problem I have with chemical treatment is the waiting time and that just takes a little conscious management of water. If there are large distances between water sources that might mean carrying enough extra water or an extra bladder, both equalling the weight of a filter.
Filters are easy enough to use and they will tackle stuff like tanin-laden water and help with some chemical/taste issues. They aren't cheap and they aren't light, but filters do allow you to get immediate gratification and can draw water from sources you can even dip water from with a cup. There is the mechanical failure factor of filters too-- break a ceramic cartridge or clog one up in the middle of nowhere and you're hosed (no pun intended), so you should still carry chemicals as a backup.
I use a Katadyn Hiker Pro, which came with some snap connector fittings. I spliced them into the tube on my Platypus so it is possible to refill the bladder without removing it from my pack. If I carried the filter in a side pocket, it would be possible to refill without even taking the pack off--- but who would miss that opportunity!
So, use chemicals for the lightest alternative. Plan ahead a bit, maybe carry an extra one liter bladder to help balance treatment time vs water supply--- treat two liters in your pack while drinking the spare liter and then treat the refilled one liter while using the completely treated two liter, etc. Treat overnight whenever possible. Use chemicals when viruses are a concern. Use a filter when hiking with a group (weight averages out) and for quick access to large amounts of water.