Sorry for poor pic quality.

in my garden, .just about anything rogue .. not planted by me.. that grows that fast to seed in spring. is not something i want to let go to seed.. else you might have millions next year ...

and youd need a million to get any kind of flower show out of it .. lol ...

there are many definitions of what a weed is.. and in my garden.. such is a weed ...

btw.. you didnt actually ask a question... just interested in a weed name.. value.. edible.. etc ...

ken

I'm curious as to the name of this plant.

It is really difficult to see the details but shepherd's purse may be?

Arabidopsis thaliana? A lot of variation in the leaves, depending on location.

I will try to get better pictures (although I pulled a lot of it already).

The flowers match Arabidopsis thaliana. There is one more common species in New York, Arabidopsis lyrata. It's very similar to, and can hybridize with Arabidopsis thaliana.
I think your weeds look closest to Arabidopsis thaliana, but can decide after comparing them.