If I transferred to UCB for pre-med, would I have to take the weeder courses, or would I finish them at my community college?
For pre-meds, all courses are weeder courses in that any grade lower than an A- harms your chances of admission to medical schools.
Also, medical schools tend to want to see at least some BCPM (biology, chemistry, physics, math) courses taken at a four year school. For those who completed most of the typical pre-med BCPM courses at community college, this means taking a significant number of upper level BCPM courses at the four year school. If your major is in one of the BCPM subjects, that will happen automatically. If your major is something else, medical schools expect you to use some of your free elective space at the the four year school to take additional BCPM courses.