Forgive me for the dissertation, but I did quite a bit of research on this a few years back for both my own model building efforts as well as a grad paper I did toward my MA in History.
Marine Paint has three primary functions: 1) First and formost, preservation. 2) Identification. 3) Decoration.
15th and 16th century marine paints would have been mostly very dark. During the late 16th up to the mid 17th century you would have seen the dark in southern European(Spain and Mediterranean countries) and lighter in Northern European/Baltic countries. By the late 17th and 18th centuries, you would have seen mostly light paints.
Why?: The elements will completely destroy a wooden vessel in a matter of a few years if it isn't properly painted, especially in the tropics. The earlier compositions were made primarily of pitch, tar, volcanic sands, broken glass(darker earlier) and pumous. This mixture was boiled together and put on hot in layers. On the bottom they would often put hair and rope shreddings/cloth fragments between layers. If they didn't do this (careening) in the tropics a couple times of year, the bottoms would become so hairy with marine life that it would cut their speed (wetted surface) down to nothing. The Portuguese and Spanish would often use the same mixture to paint the upper hull. Historically this gives the reasoning behind the Portuguese being called the "the black ships" or "the black fleet".
Why the gradual whitening? In the north, sulphers, ox tallows, and clear or lighter broken glass were used in the mixtures. As whaling became very prominent in the mid 17th century, whale oils became an essential ingredient to all marine paints. The Dutch developed cold mixtures that could be put on without the boiling which saved lots of time. So you would have now seen lighter and yellower paints. For ships that spent a lot of time in the tropics I'm sure you would have seen much less decorative and colorful paints and whatever they had out of necessity. Dark monoschemes would have been likely just as most pirate vessels are portrayed with. As standardization became more the norm in the late seventeeth cent naval vessels would have kept barrels of their colors aboard. There are historical anecdotes of naval vessels being abandoned because they were forced to patrol too long without careening and couldn't catch a fly and so eaten with worm after only two or three years service.
I won't go into identification and decoration so much as to say it was more of a nationality/naval tradition. Lots of changes in "style" over the years. Difficult to research. Lots of bright colors on southern vessels and Flemish vessels (I think personnaly to contrast the dark). The north leaned towards common mono or bi-color schemes of less brightness.
Lastly, the black on the upper clinker built area portrayed on the Wappen Von Hamburg is accurate. Earlier ships of the Hanseatic League (they also liked colorful white and red and yellow chevrons down the hull over the black), Lubeck, Brandenburg, and the other Norther German states of the time often painted the upper works of the vessel black or the Dutch green.
V/R MK
One other thing I was just thinking about that I haven't seen in our games is that most mid seventeenth century navies adopted red as the color of the inside gun-wales and often the decks as well for the obvious reasons of hiding blood and preventing panicked sailors.