To give you an idea of the weight difference, an average human IgG[1] antibody is about 500 more massive than a pretty average small molecule antibiotic like levofloxacin[2]
Their fate mostly lies in catabolism, i.e. they are broken down and the components reused. Biliary excretion accounts for a very small amount of the elimination of IgG antibodies.
[0] "Pharmacokinetics of Monoclonal Antibodies" http://onlinelibrary.wiley.com/doi/10.1002/psp4.12224/pdf
I missed it when I wrote my reply, concentrating on the immediate question (interesting psychological problem) - and then I could not edit it. It bothered me quite a bit but I did not want to write a third reply. Interesting to see how easy it is to get sidetracked on an irrelevant (albeit interesting) question, and how hard it is to get the discussion back on track.
I tried adding this quote from the linked paper:
> Thus, IgG elimination occurs mostly through intracellular catabolism by lysosomal degradation to amino acids after uptake by either pinocytosis, an unspecific fluid phase endocytosis, or by a receptor-mediated endocytosis process.
Explanation of two words in there that maybe not everybody knows:
pinocytosis: The ingestion of liquid into a cell by the budding of small vesicles from the cell membrane.
endocytosis: The taking in of matter by a living cell by invagination of its membrane to form a vacuole.
EDIT: I can still edit this comment more than five minutes later, as expected. Hmm... why could I not do that with my first comment...?