As you obtain higher rank, you'll encounter more powerful ship. In my game i got rank 12 and most of the ship i encounter are Spanish and pirate's Galleon, heavy Galleon. Heavy frigate seem to serve in national navies of French and English. Heavy Frigate is geared toward speed and combat so the cargo hold is not that big, around 3000. Heavy Galleon is good in a fight with large crew, big cargo hold, mostly armed with 48 to 54 guns, with caliber around 18-32 pounders with slower speed.
The best way to get the Heavy Frigate is to take on large number of pirates, a group of 3 to 6 pirates will give you a good chance to have it or the heavy Galleon. Don't let the number of ship scare you since it contain smaller ship too. Only one or 2 big guy with the rest are small ship that can be kill with to well aim mine or bomb broadside.
Another way is to take part in battles that are being fought. Preferably English vs Spain, English vs Dutch, French Vs Spain and pirate vs either Spain, English or French. Just look at the Avatars fighting on the map, if the Avatars are small, ignore them. When you join the battle and see your prey, stay put and see how the battle goes, when to fight is over, move closer you your prey and unleash grapeshot before boarding. Or you can destroy other surviving vessels before attacking your prey.
Lastly, obtain a bounty on your head that bounty hunter will attack you on the sea. Depend on the prize, the attacking ships could have Heavy frigate and Heavy Galleon. But this is slow since it's take quite a long time to get a big enough prize to entice bigger investment from head hunter.
PS:If you want speed, heavy frigate is quite ok. If you want fire power and cargo space with large number of crew to loots colonies with direct attack from the sea, Heavy Galleon is perfect. I have 7 of them with 356 32-pounders. Getting the ships are easy, getting the guns are the hard part.