The lines contain an example of what linguists sometimes call false concord. In the introduction to the third chapter of The Language of Shakespeare (André Deutsch, 1976), G. L. Brook writes,
Many of the differences between Elizabethan syntax and that of the present day can be explained if we remember that the Elizabethans preferred vigour to logic. (…) Shakespeare was writing for an audience, not a reader, and hence such features as false concord and mixed constructions are common in the First Folio, which reflects the familiar and spontaneous style of the spoken language.
Brook then devotes two pages to potential causes of false concord (page 65), one of which is the influence of regional dialects.
In the context of the prologue of Romeo and Juliet, it makes sense to treat "overthrows", in the sense of "downfall", as logically singular, even though it is plural in form.
In his edition of Romeo and Juliet (The New Cambridge Shakespeare, Cambridge University Press, 1984), G. Blakemore Evans provides the following gloss for "doth" based on E. A. Abbott's A Shakespearian Grammar (1869):
Southern form of third per. plur., still commonly used in Elizabethan English (Abbott 334).
Regardless of which explanation one accepts, false concord is not unusual in Shakespeare.