35 lbs is pretty big. I personally use the Burley Trailer because (to me) it seems much safer. The bike can flip and still keep the trailer upright. Not so w/ a baby seat. And a baby seat tends to make the bike top heavy, which can be tricky to maneuver, especially w/ a 35 lb kid.

My 2 year old is about the same size. Perhaps it's time for the kid's own bike? I got my kid a Specialized Hot Rock, 12" frame. She's still figuring out how to pedal.