By Art he gladly found what he did seek, A full requital of his striving pain. Art can do much, but this maxim’s most sure: A weak or wounded brain admits no cure.
I believe this is showing a weaned affection as he throughly enjoys art which could be a potential distraction to God.
I am obnoxious to each carping tongue Who says my hand a needle better fits.
As we see gender roles seem to be a big theme in this poem. In the sentence of the poem she seems irritated due to the fact people are saying her hand is a better fir for the needle which was used to sew and knit (an obvious) gender role, than it is holding a pen which she uses to write poems.
For such despite they cast on female wits. If what I do prove well, it won’t advance, They’ll say it’s stol’n, or else it was by chance.
I believe she downplays her poetic skill because it seems in this time women were not really thought of as much, as this sentence is saying if she does do well, they will believe she stole it or it just happened by chance that it became what it is.