It appears to me that opposition to marriage equality comes primarily from religious groups, in particular from the Abrahamic religions. Quoting Wikipedia:
Many forms of religions, including the Eastern faiths and Abrahamic faiths, do not support homosexual sex. Evangelical Christianity,[10] Catholicism,[11] Mormonism,[12] Orthodox Judaism,[13] and Islam,[14] 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?