Wow, so many conflicting headcanons. Here's what I've got.
The Turks are always following Aeris, she says as much. It was just their standard stalking duty that brought Reno to the church, otherwise he would have come in more force and wouldn't have been surprised Aeris' visitor has Mako eyes. His backup is crushed and he doesn't like his chances alone, so he backs off or summons medical attention (out of character for him to care about the MPs, but anyway).
After the bombing, Heidegger asks the Don to find 'a man with a gun arm', and the Don's lackey tracks Barret to sector seven, calls in with this info, and then investigates further, and is promptly caught, interrogated, and killed. All the Don and Shinra know is that Barret lives in Sector Seven, if they knew any more, they would just storm Seventh Heaven. Tifa decides to investigate (and clearly the Don doesn't know she's linked to AVALANCHE or he wouldn't let her into his manor.)
Aeris brings Marlene to her Mom's. Independently, Tseng goes to Elmyra's house, finds Aerith
and threatens Marlene to force Aerith to come quietly (otherwise she will fight, and might be hurt or killed (which is one reason they haven't brought her in sooner. He has no possible way to know who Marlene is and just thinks she's some random girl that might mean something to Aeris if threatened. He is surprised that Aeris has any links to AVALANCHE at all
They've been trying to bring her in for years, but they don't want to hurt her in doing it, and violently kidnapping her could get her hurt or killed. This time, they have leverage to get her to come quietly. It's not because Marlene is important, it's just that she can be used to make Aeris go quietly.
He goes to the pillar on the way, chats with AVALANCHE, then realises he's taunting a man with a machine gun pointed directly at him and grabs the nearest convenient human shield. It's a massive credit to Barret that he is willing to not fire for the sake of some random girl he doesn't know, when he thinks he's cornered and about to die.
Re: "Someone I loved" that's just a poorly chosen scriptwriting shortcut because the true nature of their relationship would take too long to explain.