The Mosquito was certainly capable of carrying over 2000 lbs to Berlin.
The bomber variant was specifically tested with the 4000 lb "cookie", although a more usual bombload would have been 4 or 6 x 500 lb "short fin" bombs.
The range with 4000 lbs was approx. 1500 miles, so Berlin & back with 4000 lbs would have been possible, though perhaps not at high speed, and assuming a pretty direct flightpath.
It is possible that later variants with more powerful Merlins could have carried a greater load, but whether any actually did I'm not sure.
SD