Ditto -- I've heard "lay it on thick" countless times in the U.S., but not "pile it on thick."
In my experience, "lay it on thick" conveys both a sense of exaggerated drama and an element of deception -- or, put more bluntly, B.S.
For instance, a 17-year-old girl might tell her female friend: "When that cop pulled me over for speeding Saturday night, I sobbed and told him that my boyfriend had dumped me and I just wanted to get home to my mom. The cop let me go with just a warning."
FRIEND: "But you were on the way to Melinda's party. Wow, you sure laid it on thick!"