Many forms of religions, including the Eastern faiths and Abrahamic faiths, do not support homosexual sex. Evangelical Christianity, Catholicism, Mormonism, Orthodox Judaism, and Islam, hold the view that homosexual sex is a sin and that its practice and acceptance in society weakens moral standards and undermines the family.
The Wikipedia article doesn't expand much on non-religious opposition to same-sex marriage. It appears most countries with strong anti-LGBT laws are countries with a dominant Muslim or Christian population (red shades on this map from Wikipedia), although attitudes within religion-dominated countries differ significantly (primarily catholic Spain has legalised gay marriage and 82% believes LGBT should be accepted, but in majority Hindu India this figure is only 10%). On the legal side:
Apart from arguments originating from the (Abrahamanic) old testament, what sources exist for opposition to marriage equality?