Shakespeare used a number of plurals with -(e)s, particularly when the subject consisted of two singular nouns conjoined by and.
This is not an error, but was part of the language used by Shakespeare and other speakers, both before and after his time. Although I can't read his mind and tell you precisely why he chose to write it that way, it does fit a larger pattern of usage in and outside his works, so I'm not convinced by explanations that he's simply "breaking the rules" for the purpose of rhyme.
That said, I'd rather avoid discussion of "rules" – which certainly did not constrain Shakespeare – and so of course I won't be discussing whether the rules of grammar were more or less lax in those days. Instead, I'd prefer to focus on grammar as a description of how people use language, whether it's standard or not. In that sense, Shakespeare's language certainly does have a grammar, and given that examples like this were not infrequent, I think we have to admit that the alternative plural form was, in fact, grammatical.
This sort of usage is, however, considered non-standard English today, and has been considered non-standard for quite some time, so you may see versions of Shakespeare's plays where these words have been unnecessarily "fixed".
This is addressed in A Grammar of Shakespeare's Language (Blake 2002) on pages 90–91:
These forms are often considered erroneous so that ‹-(e)s› or ‹-(e)th› are emended unnecessarily to the zero form in modern editions. [ . . . ] The use of these endings [ . . . ] with plural subjects is probably due to the feeling among speakers of the language that the third singular form was the norm and so they were applied to other forms such as the plural. This tendency is still found in modern dialects, but was driven out of the standard language by the grammarians. This applies even more so to forms in ‹-(e)s› in certain other conditions. Two nouns in the singular linked by and often have the present plural in ‹-(e)s› [ . . . ] It could be argued that the compositor or even the author was influenced by two nouns in the singular to make the verb singular so that it should be emended in modern editions; but the examples are numerous enough to suggest this is not the case. [ . . . ] Examples like this existed in English long before Shakespeare's time and continued to do so after him.
I've abridged the passage above somewhat to make the point more accessible to those interested in a quick answer, but I'll reproduce the full quote below for those who are interested in specific examples:
The standard plural is endingless like the base form: Clowds, Dewes, and Dangers come; (JC 5.3.63). A few examples of older ‹-en› survive as an archaism or a non-standard form: perishen (Per sc. 5.35., spoken by Gower as prologue), and waxen (MN 2.1.56, spoken by Puck). The plural could also end in ‹-(e)s› or ‹(e)th›, and examples are not infrequent: Which very manners vrges. (KL 5.3.209), My old bones akes: (Tem 3.3.2), Vntimely stormes, makes men expect a Dearth: (R3 2.3.35), Look how thy wounds doth bleede at many vents: (TC 5.3.85), All his successors (gone before him) hath don't: (MW 1.1.12). These forms are often considered erroneous so that ‹-(e)s› or ‹-(e)th› are emended unnecessarily to the zero form in modern editions. The use of these endings and of is and was with plural subjects is probably due to the feeling among speakers of the language that the third singular form was the norm and so they were applied to other forms such as the plural. This tendency is still found in modern dialects, but was driven out of the standard language by the grammarians. This applies even more so to forms in ‹-(e)s› in certain other conditions. Two nouns in the singular linked by and often have the present plural in ‹-(e)s›: faith and troth, . . . Bids thee (TC 4.7.52–4), Hanging and wiuing goes by destinie. (MV 2.9.82), Where death and danger dogges the heeles of worth. (AW 3.4.15). It could be argued that the compositor or even the author was influenced by two nouns in the singular to make the verb singular so that it should be emended in modern editions; but the examples are numerous enough to suggest this is not the case. When the verb precedes a plural subject, the verb may take the ‹-(e)s› ending: Then what intends these Forces (2H6 5.1.60), There comes none [i.e. swaggerers] heere. (2H4 2.4.92), depends and rests The liues of many, (Ham 3.3.14–15). Examples like this existed in English long before Shakespeare's time and continued to do so after him. None in the second example may have been regarded as a collective singular which would take a singular verb, but this explanation does not apply to other examples, just as the subject in his Braines still beating, puts him (Ham 3.1.177), could be taken to be singular since we only have one brain each so that the verb should not have ‹-es›. Such examples need not be emended.
