Weighted voting is, simply put, a collective decision making process where votes are explicitly assigned unequal weights. It's actually a quite common approach in international bodies, notably followed in one form or another by:
- The European Parliament (degressive proportionality),
- The European Council (qualified majority voting),
- The International Monetary Fund,
- UN's Security Council.
A less obvious example is proportional representation. Several countries that follow the approach for national elections also employ minimum election thresholds and/or plurality bonuses, to avoid extreme fragmentation and maximize the chance of electing a strong government respectively. Both are weighted voting elements, and adding a bit of history to the mix creates complex examples, like Cyprus:
- 56 members of the House of Representatives are elected by proportional representation,
- 24 seats are allocated to the Turkish community (but remain vacant since 1964), and
- 3 seats are allocated to the Armenian, Latin and Maronite minorities.
Moving on, a perhaps more clear cut example on a national level is single transferable vote, the approach followed in Ireland, Northern Ireland, Malta, Australia (for electing the Senate), India (by state legislatures), and... Stack Exchange community moderator elections ;)
Lastly, the US Electorate College is a prime example of weighted voting, disproportionally favouring the less populous states.