With a surviving Second Reich these are somewhat skewed measurements though.
The U.S. economy and military is as large as it is IOTL because the USA is the leader of the freeworld.
A surviving Second Reich (+ Austria, Sudetenland etc.) would sooner or later control an economic powerblock on the continent. This and the vastly enhanced ability for global power projection would probably lead to an economy at least 1/2 as big as the USA. 1/3 seems to low imho.
The military side of things is hard to measure without an exact history of the TL
My gut says:
Germany would have a "first rate second rate Navy". There would be no way for them to beat the U.S. Navy . The rationale would probably something like a modified "Risikotheorie".
Enough to hurt the U.S. Navy enough that others (Japan?) could pose a threat to U.S. naval domination in the aftermath.
Without the standoff in Europe against the Soviets the U.S. army probably wouldn't have reached the size of OTL. It might be larger than the Reichsheer in peace time (in wartime the USA would pull decisively ahead). The German army would probably be more experienced and better lead though. They might also have some nicer toys simply because the United States would be a Naval Power first and foremost. ITTL and OTL you wouldn't want to mess with the U.S. Marines though.
Air forces would be interesting. I don't think either side have a decisive tech lead. The U.S. airforce might actually be dwarfed by the Navy aviation though.
Ultimately I think the U.S. would have a smaller military than IOTL simply because there are fewer places to actually use it. Pretty certain that the U.S. Navy would still be the mean 800 pound Gorilla though.
For me I hold to pre-1914 Imperial Germany and have left A-H either intact or some split but no gaining Austria for Germany. I have no scientific value to how the USA economy gains from being the single market it is, the culture, the people, and so much more, our per capita income is higher than a Germany or Japan, and has been, but if I skew he USA slightly less to perhaps account for the brain drain and the war damage and other less tangible things I feel I can guess at it. Backing the USA into a place more like pre-1914 than 2018 or 1945 certainly calls into question if it becomes so dominant. Using a real population calculator and trying some guesses at when German demographics shift to a lower birthrate gives me a Germany somewhere from 1/3 to 1/2 as populace, I skew it lower to reflect the smaller size and different cultural climate and get an economy defensible at 1/3 as wealthy. That is a big damn player.
And I think the world may not be quite as free market so the competing trade zones are more frictional, but you are correct, I guess at a European Customs Union led by Germany roughly covering much of modern Europe, not fully the EU, but not far from it. I have the USA closer to Germany and more at odds with the British, Japan for me looks more decaying like the old Soviet Union, France still fiercely independent but more like the UK hoping for a place in Europe yet not less than the (more than) equal she still wants to be, etc.
I think the global trading nations have arguments for strong naval power to safeguard trade, especially where the world is multi-lateral and no one power is trusted to be the policeman. Here I find the USA a peer but not having the same need to project power on every ocean or plan for wars in more than one region, so I roughly cut the USN in half to return to a USA who is no weakling but does not need to be equal to none. Germany is a similar boat but I allow for a lingering continental mission, maybe a reduced USSR or lingering antagonisms with France or Russia or whomever. Germany could be about 1/5th the strength of the modern USN here but it is a drain, manageable but under review endlessly, rather like the RN got whittled down. The British Empire looks a little stronger if all the Dominions can agree, etc., but the RN itself is more like OTL than it should be.
Without a WWII the USMC would be about two Brigades worth and without WWI they barely have the amphibious mission we know, instead I think they are more raiders like the RM. The USAF is more continental air defense and strategic bombing, the rest is an Army mission, so the US Army looks more like the modern USMC and likely has independent tactical air. This is a more modest and more expeditionary Army, the USA is not the global cop, if it needs more weight it must call out the NG. These are my guesses.
A lot is subject to changes and other influences in the century after 1918, without the same wars and the same bipolar alliance system, things get more and more guided by feel and less and less familiar. In fact I have scaled back to 50 years out because things get so hard to meaningfully guess.