The Internet is getting bigger and websites are getting larger. This means that web browsers have become larger to cope with all these new sites, based on the assumption that everyone has a new computer and a fast Internet connection to deal with it.
However, not everyone has a new computer or have a decent fast connection, a lighter web browser is what you need.
Enter Light which is a cut down version of Firefox. It supports the extensions that Firefox is famous for (adblock plus is a must these days) The 32 bit version even works on Windows XP.
Another popular choice is Midori the cut down version of Chrome. It is light weight and fast but it still has the memory hogging problem Chrome has. The Great Suspender is a great extension to manage tabs. It suspends those that are inactive and saves memory.