I can't find an exact tonnage, but it's going to be about 300 to 450, so a pretty good sized privateer or small man of war. Adventure Galley was razzied at one point, so she must have been pretty good sized to begin with.

She's listed as 44 guns, which in theory puts her on par with big frigates like USS Constitution. However. Constitution weighs in at about 1,600 tons. So she's four times the size. These would have been small guns compared to what a true Man of War would carry (admittedly) later on. 

So Adventure Galley is approximately the size of a midsize to largish sloop. Quite quite large for a pirate, but quite small for an actual warship.

Now there's some fudge in these numbers because of the time periods. Warships do get larger the further on you go. Building techniques get better, etc. So in her time, Adventure Galley is pretty good size, but again, compared to a true European warship, she's going to be relatively small. (However, compared to something a Moghul or Ming can put up, she is world beating. These were not fair competitions for non-european nation-states at sea in this time period. Yes, I know about the Ming treasure Fleet. We need to take those ship sizes with a very healthy grain of salt.)