The poem on this gravestone in RI refers to "Mary's part." What does this phrase mean?
It is a widely used epitaph of the time for beloved wives (see here and here), and seems to refer to Luke 10:38-42: (New International Version (NIV))
At the Home of Martha and Mary
38 As Jesus and his disciples were on their way, he came to a village where a woman named Martha opened her home to him.
39 She had a sister called Mary, who sat at the Lord's feet listening to what he said.
40 But Martha was distracted by all the preparations that had to be made. She came to him and asked, “Lord, don't you care that my sister has left me to do the work by myself? Tell her to help me!”
41 “Martha, Martha,” the Lord answered, “you are worried and upset about many things,
42 but few things are needed-or indeed only one.[a] Mary has chosen what is better, and it will not be taken away from her.”
By "Martha's care" is meant that the deceased was painstaking in her care of home and family; and by "Mary's part" is meant that she loved Jesus devoutly.
Here is the King James Version for Luke 10:38-42, explicitly referencing "and Mary hath chosen that good part":
38 Now it came to pass, as they went, that he entered into a certain village: and a certain woman named Martha received him into her house.
39 And she had a sister called Mary, which also sat at Jesus' feet, and heard his word.
40 But Martha was cumbered about much serving, and came to him, and said, Lord, dost thou not care that my sister hath left me to serve alone? bid her therefore that she help me.
41 And Jesus answered and said unto her, Martha, Martha, thou art careful and troubled about many things:
42 But one thing is needful: and Mary hath chosen that good part, which shall not be taken away from her.