Blackberries, Raspberries, dewberries, and bristleberries are all part of the genus Rubus common to North America.
These are thorny shrubs with long 'canes' that produce fruits annually, with more than 1300 varieties. They are a relative of the rose plant. Indigenous people utilized them for their cooking, and the leaves, bark, and roots were made into medicinal teas.
Nicassius de Sille notes them as 'weeds' because they are so plentiful: " The weeds consist mostly of strawberries, catnip and blackberries."
See a detailed article on the archeology of plant life in New Amsterdam by Joel Grossman, PhD. here. Courtesy of the Holland Society of New York.