Why did constantine legalize christianity?

History isn't actually quite sure why Constantine decided to convert the Roman religion to Christianity. 
History can prove multiple guesses as to why, so I'll list a few of them:

Constantine converted for political purposes:
Frankly, this just confuses me. Constantine converted to Christianity indeed, but he would've had nothing to gain from this. Before he converted, Christians were hated, as well as Christianity. There was definitely more of a downside than an upside. 

Constantine converted because he personally believed in Christianity. 
This theory is logical. Constantine's father wasn't like him, meaning he made no attempts to support Christianity, so Constantine would've had to have been influenced by someone else. At that time, the silk road was blooming and thriving, and missionaries from all religions traveled to other nations/empires through the use of that trade route, including Christian Missionaries. It seems likely that Constantine was influenced by one of these missionaries at a young age, and became a believer in Christianity from then-on. 
Later on, there was at least 1 priest in his private circle (most trusted friends/advisors). 

The most likely reason is that Constantine was indeed a believer of Christianity, which is why he legalized it. 

~Hope this helps m8