The UN has a number of programs which cost money; even just the maintenance of the building and staff costs money. There is a formula they use to "harmonize" contributions by population, gdp etc.
From the documents, it looks like Tuvalu contributes $ 2,500 p/y to the Working Capital Fund (i.e. reserves) and about $ 40,000 p/y to the regular budget (which is periodically modified and approved depending on needs of the various programs, and collected yearly from member countries, with unspent leftovers returned to them).
If these look like paltry sums, it's because they are. No wonder the Gates Foundation is squarely in the top-20 UN donors.
For comparison, some of the biggest contributors are the US (55m to Working Capital Fund, 750m to yearly budget), China (38m and 500m) and Japan (20m and 220m), although the highest per-capita contributions amoung sizeable countries are Norway and Sweden.
Island sells web address to buy UN membership [0]
[0] https://www.theguardian.com/technology/2000/sep/10/business....