It may be a Chenopodium.

Definitely.

if it free seeded itself into your garden ...

and has a ka-jillion seeds.. as you note ...

what more do you need to know ... it safely falls within the definition of WEED ...

unless you want a half a ka-jillion more next year

ken

Thanks Carol and rugby. Ken, yeah I know I just wasn't sure so thought I'd check in. I sowed some flower seeds and, although I did not recognize this one, just wasn't sure. We just got a good, soaking rain so I'll pull all those crazy seed-headed weeds over the weekend.

Thanks again for the help. Mary

But not Chenopodium album, is it? C. album is the only one I'm familiar with, and it really doesn't look like that.

C. murale?

Two options for this plant are C. murale (as nonmember said) and C. berlandieri. Both species are found in Arizona. If the bottom sides of new leaves have significant mealy pubescence (white splotches), that suggests C. berlandieri. If the bottom sides of new leaves have minimal mealy pubescence, then C. murale is more likely.