Hatton was on five under for the day with five holes remaining to put him atop the provisional leaderboard at 12 under.
Romain Langasque was five shots adrift after 16 holes before conditions forced organisers to suspend the round.
Sharing provisional second with the Frenchman was overnight leader Rory McIlroy, who was one over for the day with four holes still to be completed. And two who managed to make it to the clubhouse, New Zealander Jason Scrivener and Thailand’s Jazz Janewattananond.
Janewattananond and Scrivener were out early to finish their first rounds on Friday morning after Thursday’s fog delay of almost three hours forced them to play catch up.
Hatton is aiming for a fourth Rolex Series title in this event, the first of three tournaments being staged in the Gulf.
He began his second round one shot off his Ryder Cup teammate McIlroy after assembling a fine opening 65.
The 29-year-old followed up the two eagles he had made on day one with another from 22 feet on the second hole.
After dropping his first shot of the tournament at the next he hit back, producing a run of four birdies.
He was going in search of his tee shot into a bunker at the 14th hole when the siren sounded a premature halt to the round.
“I’m obviously in a great position at the moment,” he said.
“It was certainly tough out there, so I’m really happy to be five under.
“I held some nice putts and there were a couple of par putts towards the end of my round – nice to hold them and keep a bit of momentum going.”
On the prospect of a busy day at the office on Saturday, Hatton added: “It will be fine. I’ll just try and stay loose and see how we go.”
Langasque was almost celebrating the first hole in one of the new Race to Dubai season, his tee shot at the par three 15th whistling past the hole.
Defending champion Lee Westwood bogeyed the 13th and 14th before play was suspended to lie nine shots off the lead, with world number three Justin Thomas on the projected cut mark of one under.