Coconuts can get around, and weight ratios don't even enter into it. The fruits don’t exactly travel between different climates season by season, but they are quite capable of traveling on their own.
Coconuts come from one of several plants that spread themselves using drift seeds, which can travel for thousands of miles over by floating in the ocean until they land on distant shores. If a coconut falls into the ocean, its buoyant husk allows it to travel wherever the ocean currents lead it.
The question remains: could a coconut possibly migrate from its native tropical climate to a more temperate region, such as (and this is just off the top of my head, mind you) the Medieval Anglo-Saxon kingdom of Mercia, located in modern-day England? To answer that, we need to take a look at where coconuts grow, and how ocean currents work.