It's not entirely true to say the world population is increasing. Yes the number of people is going up but not uniformly around the world. Developed nations often struggle with population decline as economically comfortable educated societies seek to have less children. This has been an issue for a while in some western nations who have been using immigration as a way to fill in the gaps. Other more recently developed blocks are just now facing population gaps in their latest generations and are currently figuring out a way to stabilise things.
As someone once said, "the rich get richer and the poor get children" and boy is this true. It is in the poorest most economically desperate nations where population growth tends to be the most out of control. Short lifespan, terrible infant mortality rates, lacking social mobility, low rates of education and poor sexual freedom lead to a huge boost in the numbers of children. Families are large because of a need to have some kids who will manage to make it to wage earning adulthood. This terrible trap of human want has been around for as long we've had towns to put people in.
I'd be tempted to say that all you need to do to combat spiralling population growth is to equalise wealth around the world so that poverty and want is eliminated, education is universal and excellent healthcare is freely available to all. Unfortunately I think that sentiment is even more controversial for some people than the Stop at Two campaign!
Sadly space colonisation isn't ever going to be a solution to Earth's population problems.
However, the technologies developed from learning to live on alien worlds like Mars can be brought back to Earth and applied here. The same abilities that would allow for sealed self sufficient habitats on Mars could be applied to building self contained cities in the middle of the deserts. In frozen wastes, or even beneath the sea. Humans may be able to live in parts of the world before considered off limits, and all without adding to levels of pollution. A possibility like that would make any planetary exploration worth the cost.