I have been working with jQuery for a while now and i can tell that the 26kb that it weights is a really small price, and like many other files only needs to be downloaded once (after that it gets loaded from the cache).
1. [Huge list of plug ins]
There are many plug ins for different solutions: galleries, validation, ajax, file handling, etc. Also you can use plug ins to [fix CSS problems]
2. Browser compatibility
Although i was not able to find a documented list of the fixes jQuery applies, you can always go over [the source code], it is very well documented and divided so you can see what happens when.
3. Consistent
While you work on different projects, if you keep using a library, you will learn more from it each time and work faster.
4. Community
jQuery probably the biggest in javascript libraries, and that comes with a lot of advantages like support, tutorials and plug ins.
5. DOM Manipulation
jQuery sintax makes it very easy to manipulate the DOM, instead of document.GetElementsByTagName("tag") you can do $("tag")
Bottomline
I can tell jQuery has saved a LOT of time for me, and made things easier to deal with, i would totally recommend using a library.