At the end of the day (or two weeks) the country with the most medals tops the table, but for a little fun, don't let anyone tell you either the US or the UK won! (at least by capita or GDP.)
Total medals per capita (2016 Rio Olympics)
Rank Country Medals
1 Grenada 1 106,825 population 106,825 population / medal
2 Bahamas 2 388,019 194,009
3 Jamaica 11 2,725,941 247,812
4 New Zealand 18 4,595,700 255,316
5 Denmark 15 5,676,002 378,400
19 Great Britain 67 65,138,232 972,212
43 United States 121 321,418,820 2,656,353
http://www.medalspercapita.com/#medals-per-capita:2016Total medals (weighted) by GDP (2016 Rio Olympics)
Rank Country Medals Weighted Medals GDP GDP per Weighted Medal1
1 Grenada 1 2 0.82 0.41
2 Jamaica 11 32 15.07 0.47
3 Kenya 13 37 33.62 0.91
4 Fiji 1 4 3.81 0.95
5 Armenia 4 10 10.25 1.02
36 Great Britain 67 171 2431.59 14.22
64 United States 121 296 15094.00 50.99
http://www.medalspercapita.com/#medals-by-gdp:2016Or this:
http://www.telegraph.co.uk/olympics/2016/08/21/rio-2016-alternate-medal-table-how-countries-rank-when-we-adjust/