Having read the 2007 winner, Sally Van Doren's Sex at Noon Taxes, some months ago, my first thought is that the Walt Whitman judges must have a soft spot for sonnets, as all of Van Doren's poems in that volume were variations on that form, and a good many of Wiese's are as well. Those that are not fourteen lines long tend to be 28 or 42 lines long, and feel like stacked sonnets.
Wiese's poems remind me very much of the sort one frequently encountered in the New Yorker in the Alice Quinn era: built on precise observations, employing a fairly subdued emotional palette, craft-conscious, well-behaved, frequently concerned either with New York City or with whichever small middle-American town the poet grew up in. Their only flaw is that they fail to be deeply interesting.
Wiese has an interesting idea in here -- that underneath the elaborate human artifice of New York City, and occasionally and surprisingly visible, is a natural substrate of soil, rock, water. This notion has an appealing kind of stoner wisdom to it, and I wish she had been a little less risk-averse in pursuing it.