PREVIOUS ADVICE 
I am interested in doing research on the long-term affects of long-distance hiking. I am proposing to hike the Pacific Coast Trail (from Mexico to Canada) over a period of 6 months. I would like to do preliminary tests on muscle density, metabolism, fat content, lung capacity, bone density, etc., and then see how those change during and after hiking the trail with a backpack. I am not really sure what category it would fall under, so I can't really figure out where to look for funding. Thanks.
Many research projects like the one you wish to do come under the categories of biomechanics, sports medicine, physiology, stress training, muscle, and orthopedics, to mention a few; and many researchers find financial backing specifically for hiking studies: For example, scientists at Oklahoma State University compared the heart rate of hikers with and without the use of hiking sticks; a Danish group compared the hiking performance of elite sailors; others have looked at how specific knee muscles change in uphill and downhill walking. But these projects use groups of individuals and very well-controlled settings.
Experiments that only use one individual are difficult to find support for because that person alone may affect or skew the outcome of the study. You may have to incorporate your hike with other studies so that it constitutes just part of your research plan. For example, if you say you're going to study a number of people that do the trail, you may be on to something.
The National Heart, Lung, and Blood Institute  at the National Institutes of Health has funded research on the effects of walking and running--one study they funded proposes to compare the rates of heart disease and cancer among 68,000 runners and 68,000 walkers! The National Institute on Aging  supports research on fitness and the effects of exercise on specific cohorts.
The American Society of Biomechanics  provides links to graduate biomechanics programs at universities across the country as well as contact information, faculty interests, and department information. Call around, explain your idea, and ask what their sources of funding are or if they have research plans that are similar.
Be ready to explain why you think this hike is important, what questions you hope to answer, and what techniques you will be using. Agencies will want to know what new information your study will provide and how it relates to their overall aim and mission.
I assume you're referring to the Pacific Crest Trail, which runs 2638 miles (4245 kilometers) from Mexico to Canada, and not the California Coastal Trail, which only winds a mere 1200 miles (1930 kilometers) along California's coastline.
The Pacific Crest Trail Association  predicts that the trail can be completed in the time frame you mention--5 to 6 months--if you can blaze an average of 20 or more miles (32 kilometers) a day. Roughly 200 happy hikers start out on the Pacific Crest Trail, but only a quarter actually finish. Are you in that group? Any funding source may want to know your chances of finishing.