Yesterday the House Committee on the Judiciary, Subcommittee on the Constitution, held this hearing on the proposal to give DC representation in the US House, along with adding an at-large seat to Utah (to preserve partisan balance). By clicking on the link, you’ll be able to download the testimony of the four witnesses, who were split on the constitutionality of the measure. (See also this Washington Post report.)
As I understand it, there are two constitutional issues. First, can D.C. get a voting representative in the House, if it is not a “state”? I have never looked into that question, and I’ve got no opinion on it. Second, does giving Utah voters a second vote for an at-large seat violate some kind of one person, one vote principle. On that question, I think there is no constitutional problem. No one in Utah’s voting power would be greater than any other person’s voting power. I just don’t see the issue being a serious one at all.