What are these sweets from 16th century?
I think user23614's comment is correct. They're ragged comfits, sugar coated seeds or spices. 

These two paintings by the German painter Georg Flegel, have similar objects depicted, and are described by two different sources (Sugar-Plums and Comfits, Sugar Plums Demystified) as being ragged comfits:





They're apparently not very common these days, surviving in the form Pistoia confetti, also known as birignoccoluto. They're apparently primarily given out as treats at weddings. Coincidentally the Clara Peeters painting you're asking about may be, according to one interpretation, depicting the ragged comfits as a treat at a wedding.