Yes, typical fiberglass can absorb water but in your case you said it correctly "overblown". You got my curiosity going and I did some reading and typically, absorption is 1-3% on a surface in a period of 3 -5 years. this is usually a problem with some boats that sit in the water all year and have bilges constantly soaked with water. Most concern is gel coat blisters. The fiberglass turns pink as in this article:

http://www.marinesurvey.com/yacht/WetLaminate.htm

If you absorbed 1/8 of an ounce of weight I would be highly surprised. Water also dries out too so if you are having nightmares, leave it in the sun for a few days and you are back to where you started.

Sometimes when I pick up my boat, especially at the end of a paddle It feels like it's really heavy too. One glass test I read said they actually had to boil the water to get any absorption at all. Generally for a kayak, the answer is no, you do not absorb water.