Compare your plant to Hibiscus coccineus.

Here is a link that might be useful: Google image results

Thanks Jeanne, but my plant is more tree-like with a long central stalk, not a bush, and the leaves are wider and more handlike. The Hibiscus had much more skinny leaves. Also, my plant has no flowers (yet?). Thanks for responding.

It could be a Mulberry tree.

Ditto Mulberry, Morus alba in fact.

Here is a link that might be useful: {{gwi:168161}}

http://www.forestryimages.org/browse/subthumb.cfm?sub=6050

Here is a link that might be useful: {{gwi:168162}}

Thank you all for your input. I think mulberry is correct! That makes the most sense. I would have likely grabbed some fresh mulberries and planted them a while back. Or perhaps the birds helped me?

But...would you consider this to be a weed?

IMPACTS AND CONTROL:
Impacts:
Native vegetation: There is widespread concern over white mulberry's hybridization with the native red mulberry ([18,153,171,174], review by [30]). In Ontario, resulting hybrids were more similar to white mulberry parents, suggesting the potential for a local extinction of red mulberry [18]. In 1963, white mulberry was more common than red mulberry in southeastern Kansas [55]. There is also some concern in the mid-Atlantic region that white mulberry may transmit a harmful root disease to red mulberry [153].

Though it generally grows at relatively low densities, white mulberry has the potential to exclude native vegetation (review by [51]), particularly where it grows in dense thickets. However, as of this writing (2009) there was little published information documenting this impact. On a dredge spoil island in South Carolina, 95% of a 22.5 acre (9.1 ha) area was covered by a closed-canopy, even-aged stand of white mulberry. No understory was present [120]. White mulberry also established in thickets in limestone areas in north-central Texas [32], though no impact on native vegetation was reported.
White mulberry infestation.
Photo by Ohio State Weed Lab Archive, The Ohio State University, Bugwood.org

White mulberry may have allelopathic properties; in laboratory experiments, white mulberry leaf leachate inhibited the germination of India mustard (Brassica juncea) [2].

Other impacts: Spreading white mulberry roots damaged pavement and curbs in San Francisco (review by [33]).

Here is a link that might be useful: Quacks like a Duck

Thank you! I'll pull it and compost it.

If it's not too late to pipe in - is there any way you might've planted a couple papaya seeds?

Susieqsie,

Thanks for your input. It does look like a papaya indeed! And I could have planted those seeds as I do eat a lot of tropical fruit. But the stalk appears more like a mulberry. Plus, I already composted it!