This poem's meter is marked below. Each stressed syllable is marked with uppercase letters, while each unstressed syllable is marked with lowercase letters. Each foot is separated with a vertical line.

I THOUGHT/ they LOVED/me, DID/ me GRACE/

To PLEASE/them SELVES/ 'twas ALL/their DEED/;

God MAKES/, or FAIR,/ or FOUL/, our FACE/;

If SHOW/ing MINE/ so CAUSED/ to BLEED/

My COUS/ins' HEARTS/, they SHOULD/ have DROPPED/

A WORD/, and STRAIGHT/ the PLAY/ had STOPPED/.

Each line starts with an unaccented syllable followed by an accented syllable. These two syllables together make up a foot; the end of each foot is marked with a vertical line. This type of foot, which has an unaccented syllable followed by an accented syllable, is called an iamb. Therefore, this poem is written in iambic verse. There are four feet in each line of the poem, so this poem's meter is iambic tetrameter because a tetrameter is a line with four feet. The more common type of verse is iambic pentameter, which has five feet, each with an unstressed syllable followed by a stressed syllable. Iambic pentameter is a relatively natural meter form in English, and many poems and plays are written in this type of meter.  

The rhyme scheme for this poem is ABABCC. That is because the first line ends with "grace," and the third line ends in "face." The second and fourth lines end with "deed" and "bleed," and the last two lines (referred to as a couplet) end with "dropped" and "stopped." This type of rhyme scheme is called an English sestet, and it was originally a Sicilian rhyme scheme that was popularized by Shakespeare in his sonnets. 

I thought/ they loved/ me, did/ me grace/

To please/ themselves;/ 'twas all/ their deed;/

God makes,/ or fair,/ or foul,/ our face;/

If show/ing mine/ so caused/ to bleed /

My cou/sins' hearts,/ they should/ have dropped/

A word,/ and straight/ the play/ had stopped./

In the above, the stressed syllables are bolded, while the unstressed syllables are not. A meter contains several feet of stressed and unstressed syllables. (In poetry, a "foot" refers to two or more syllables, one of which is usually stressed and one of which is usually unstressed.) Since we have an unstressed/stressed pattern in each line, the meter is iambic. Other meters with two-syllable feet are trochaic (with stressed/unstressed feet) and spondaic (stressed/stressed feet).

Also, we have four feet in each line, so we would classify the meter as iambic tetrameter. This means that the feet are iambs—combinations of one unstressed and one stressed syllable—and there are four per line (thus tetrameter, because the prefix "tetra" means "four"). The rhyme scheme is ABABCC. This means that the first line rhymes with the third line, the second line rhymes with the fourth line, and the fifth and sixth lines rhyme with each other. The rest of the poem also shows this rhyme scheme.

They, too,/ so beau/teous! Each/ a queen

By vir/tue of/ her brow/ and breast;/

Not need/ing to/ be crowned,/ I mean,/

As I/ do. E'en/ when I/ was dressed,/

Had ei/ther of/ them spoke,/ instead/

Of glan/cing side/ways with/ still head!/