Ah, thats an interesting question. I assume you really arent trying to carry water, but instead are taking short stops at streams to fill up.
Some filters are pretty light. The Katadyn Hiker Pro ($80), for instance, weighs just 11 ounces. Not intolerable if you carry a fanny pack, which surely you do in order to carry some snacks and a light jacket. But then, you specifically reference a purifier, which by definition kills viruses and things like that, in addition to the usual giardia and other water-borne bugs. The thing is, I am not entirely convinced you need that in the Cascades. At least, Im not aware of any reports of water-borne viruses hitting hikers around there. So I think in most cases a filter alone is fine.
You could alternatively carry an MSR Miox Water purifier ($140), which uses an electrical charge to create a salt-based purifying agent. It kills viruses and bacteria in 15 minutes, giardia in 30 minutes, and cryptosporidium in yes, four hours. Which is a problem, as crypto IS something you might encounter. And its something that a filter would whack pretty easily.
In my view, to be totally safe, you carry a light filter, then a bottle of MSR Sweetwater Purifier ($10, 2 ounces). The filter gets the things such as giardia and crypto, the purifier whacks the virusesand does so very quickly. You can filter, add the purifier, give your bottle a few shakes, and drink.
Stay safe out there!