I have been running a one on one campaign for a few months now (finding players in the area has been downright disheartening). The campaign itself has been going wonderfuly well RP wise (being able to focus on a single character), but has been a stumbling block for me with rewards.

At first I was favoring the side of caution and awarding less than I normally would... until the player questioned why he was only getting about half the rewards listed of equally dangerous encounters as those in Purge the Unclean, for doing more than twice the work. After reasoning through it with him, and him making some very valid arguements that he was only asking for npc help when it was his only option, I started upping the rewards to more on the level of those listed for similar events. However, due to the fact that I am able to run the games more often than I normally would with a larger group... his power level took a rather dramatic upward curve and I now have a rank 6 psyker on my hands.

I was curious how other GMs would handle rewards in such an instance of a one on one campaign?

Well, not on the "xp per session" schedule. The core rules have system for "rewards per encounter". Or "key encounter", as I would favor it. It the pc manages to achieve X, he will get Y experience for it.

I agree. If your PC is able to achieve certain things, give him rewards respectively. As for a high powered pysker? Put him up against some Nulls and a couple of NPC's who are combat oriented to back him up. Make it interesting by restricting him. Right now in one of the several campaigns I am playing in, one of my characters is a Pysker. He has an inhibitor in him right now, where he can not use any of his abilities until its removed. This has forced me into some VERY interesting role playing scenarios, not to mention desperate to get the **** thing out!