Obadiah wants what Tony has.
There is a fair bit of speculation in this, because we don't really get to see all the background on what the Ten Rings is up to besides that they seem to get an awful lot of gear. No other random faction seems to get its hands on Stark weapons that we see, so we're not really sure if Obadiah was double-dealing all around, and he appears to be treating it casually enough that he should have gotten caught much faster if he was.
What we do know is that Obadiah arranged with them the attack on Tony's convoy – we see the video they send him (that Pepper finds), telling Obadiah he should have told them who they were killing and that Tony will now work for them. This probably corresponds to the first stockpile they get that Tony destroys – he gets them the weapons to do the job and a fair bit besides as payment, and once Tony's gone he gets to take the company without a man-child to look after.
Except that in the aftermath, Tony invents this invincible walking tank suit. It's a weapon sellers dream – total protection, utter domination in a fight, flexible and mobile. Armies can't print enough money to buy that (proven by the second movie, where lots of people try). Now he's got something even better to hunger for.
So my belief, given Obadiah's later actions, is that the Ten Rings getting resupplied with Stark weapons so quickly is a second bargain. Obadiah wants Tony's suit tech before anyone else. He has a dubious ally in the area, but if he can string them along enough with more gear, they can help him track it down. As soon as he has it, he has enough of a military team that he can clean up the entire group, take the suit, and wipe clean any lingering evidence that he ever dealt with them. Anything else he can spin – lots of things happen in a war, and what bits the news reporter catch can be explained as stolen weapons (which I kinda think Tony presumes on his escape – he has a lot on his mind surviving and all, or the size of the stockpile might've caught his attention a lot faster).