Re. assessed, rather than voluntary contributions, this article goes into the funding calculation basis, for the UN as a whole (the WHO being part of the UN). The reason it's relevant is that, in political discourse, the US's share of UN contribution often comes up and it is definitely part of the general pattern of discussion on this type of subject.
Roughly speaking it seems to be based on % of gross world income, adjusted for debt level and wealth/poverty at a per capita basis.
From that POV, it is useful to remember that China's GDP sits around $10K/person, while the US sits at $65K/person. While GNI stands at $18,357,322M US vs $11,374,227M China.
I.e the US has almost twice the share of world income and its per capita basis is 6x. Debt can't figure too much into this, or else Japan and Italy would drop lower.
Basically, citizens of richer (per capita) countries pay (quite a lot) more per head than citizens of poorer (per capita) countries.
Edit: as this seems to cause some confusion...
To quote a comment:
by that logic, the biggest donors would be micro-countries like Luxembourg, since they usually dominate every "per capita" ranking.
Yes, and Luxembourg (112K$ GDP/person) is probably one of the biggest contributor per person. But since there are only about 600k Luxies adding up all their contributions would not dominate world rankings.
Let's pick Bangladesh($2K GDP/person) to do some comparisons. Let's arbitrarily pick some numbers and say that that each Lux. is assessed $50: 50 * 600k => $30M. On the other hand, there are 160M Bangladeshis, but the country as a whole is quite poor. So let's say each Bang. gets assessed $0.05, 1000 times less than each Lux.
Then Bangladesh pays $8M @ $0.05/person.
If that goes up to $0.50/person (1/100th the Lux. rate, but remember they are also only 1/60 as wealthy so they're only getting a 30% "discount").
Then Bangladesh pays $80M, much more than Luxembourg's $30M.
In neither case is the big question about only just the gross Luxembourg /Bangladesh national GDPs. It's mostly about wealth per person multiplied by the number of citizens.
Now, don't quote me on these $50/0.50/0.05 numbers, I just picked them to run through the math illustrating outcomes. The linked article explains it in more in detail. In the specific case of Bangladesh, as an LDC (Least Developed Country), it gets an ever bigger break in any case, being limited to .01% of the UN budget, max (roughly 5M$ out of 50B$).
The US is in its particular funding position because it is both one of the top-decile wealth per citizen (#7 in fact) and because it is a very big country (#3 after China and India) so per person assessments add up. When China starts nearing the US per person wealth, it will totally shoot up the contribution list. So, if the US stridently limits itself to max 20% for example they may come to regret it when China's bill ends up higher.
Also, if you look at the overall contributions, and you take say Germany, Norway or Canada's contributions, considering their sizes, the US's UN funding portion seems rather less exceptional.
Note: quartz, where I got this from has a left-center bias, with high factual accuracy rating from mediabiasfactcheck. I suppose it would be better to find a fully unbiased, but those are getting hard to find these days and I am lazy.