I've met people who were "serious" about cutting pack weight. They cut labels out of their clothing, trimmed the corners off maps, drilled holes in their tooth-brush - it was intense. They put a lot of time and effort into those few ounces that they saved. Sadly, they didn't put a whole lot of thought into it. If they're "serious" why were they still using a five pound synthetic sleeping bag, a seven pound backpack and a twelve pound tent?! Ok, I might be exaggerating a little but when it comes to making serious reductions in pack weight, you need to look at all of your gear as a whole. Eventually, trimming maps might make sense but ONLY after every other option has been exhausted.
The Big Three
To see the biggest return on your reward, begin with your backpack, sleeping bag and tent (shelter). These are three pieces of gear where you can cut pounds - not ounces. And it's also important that these three pieces of gear work together. You can't switch to an ultralight backpack before you upgrade your other gear because the old stuff simply won't fit and the pack won't be comfortable with all that weight in it.
On my PCT thru-hike, my backpack (a modified GoLite Speed), sleeping bag (a Nunatak Akula) and tent (custom, home-made) weighted less than three pounds. All three of those pieces are about as light as you can get with a good balance of quality. Even though I was hiking 2,658-miles that summer, I didn't need over-built bomb-proof gear. And you won't need it on a weekend, week-long or multi-thousand mile hike either. Take care of your gear, and it will take care of you.
While you will spend more for an ultralight sleeping bag, you will actually save money with many ultralight packs and (sometimes) shelters. Yes, some ultralight gear gets ridiculously expensive but by making an investment in this gear up front, you will be able to make progress without spending a fortune.
Remember - begin where you can cut pounds, not ounces. Then if you still want to go further, I'll share some tips and tricks later on to make smaller adjustments.