The idea of the "test curve" , the pull needed to bend the tip at right-angles to the butt, was developed by Richard Walker, who made the first purpose-built carp rod, the "MkIV" and used it to catch the 44lb carp which held the record for ages. This was beaten in the mid '80s by a fifty-one pounder taken by Chris Yates on the rod's lighter brother, the MkIV Avon.
The idea of knowing a rod's test curve was to give a guide to its safe range of line strengths and its best casting weight. Walker reckoned the line range at five times the test-curve, plus or minus thirty per cent, but later, most found they could stretch it to a minimum of three , an optimum of five, and a maximum of eight times the test curve. Few quibble with his casting weight calculation of one ounce per pound of test-curve.
Walker took his big carp on a 1.5 lb test-curve rodmatched with 12lb line, Yates caught his on a 1.0 lb test-curve rod, and IIRC, 6lb line.
The trend for two to three-pound test rods is to do with modern bolt-rigs, which need a heavy lead to ensure self-hooking; these in turn need heavy rods to cast them.
It'slittle to do with the size of fish, except in extreme hit-and-hold situations.