An elaboration on either Schnozzleberry or Skallagrim's concepts - or both, would be fascinating.
One additional point that occurs to me is this: if we assume that the associated states I suggested only contribute to the federal treasury via a basic national tarriff, and that the rate of that tarriff cannot be increased without the agreement of the associated states (and I
doubt they'd accept otherwise), then we end up with a bit of a funny situation. Congress has a tarriff, but cannot raise it easily. It cannot raise it for just the core states, either, because if there is no free trade between all the states, the whole union is pretty useless to begin with. (That issue was a big point at the outset, and presumably the associated states getting to veto a higher tarriff is 'traded' for an article outlawing any and all restrictions to trade between the states.) Now if congress raises the tarriff for just the core states, all foreign trade will just arrive at the associated states, and flow into the core states via that route-- the higher tarriff wouldn't apply at all!
So all this means: the tarriff, the one tax that basically funded the federal government until the mid-to-late 19th century... can't be raised effectively. That probably means a
much sooner introduction of direct federal taxation (property tax, maybe?) in the core states. That's an interesting divergence right there.
On the flip side, the associated states can't raise state tarriffs, either, which would be useless for the same reason. So if they want to give their own governments more funding, they'll have to introduce additional state taxation, too. And they'll pretty much have to, if they stay out of the bulk of federal legislation. They'll have to set up their own organisational structure(s). And pay for them.
So tax types and tax rates are probably going to vary wildly, but in both the core and the associated periphery, we'll likely see direct taxation much, much earlier. Food for thought!
Similar to the Federal City / Urban State idea a compromise to the small vs large state issue could be an agreement to split states that grow above a certain size.
This would be more likely to occur with urban areas.
Considering that Wyoming has fewer than 600,000 inhabitants, and New York City has over 8,5 million... trying for anything like parity would have some major implications for NYC. Of course, that also play into the suggestion by
@DominusNovus that a 'Federal City' would get only one senator. What, Wyoming's fewer than 600,000 get two, while NYC's more than 8,5 million get one? Seems a bit strange... Nevertheless, the basic idea of splitting states up is not a ludicrous idea. One might combine division and fusion, splitting off major cities to become 'urban states' and merging thinly populated areas to become territorially vast 'rural states'.
(My personal suggestion for the issue of over- or under-representation is, as always, to simply devolve as many powers as possible. If typically progressive urban areas and typically conservative rural areas are pretty thoroughly divided from each other, and both get to decide about 90% of policy for themselves... I think you'll prevent a
lot of political deadlock.)