Here's a popular loop hike around Weavers Needle from Peralta trailhead. The direction of this loop is up the Bluff Springs Trail for 2 miles. Take the Terrapin Trail north through Needle Canyon on the east side of Weavers Needle for 2.9 miles. Crossover on the Dutchman ( 1.1 miles ) to the Peralta Trail ( 6.2 miles ) and bring it home.
The whole loop is a rollercoaster ride with two minor ascents to note. First comes the immediate haul up the Bluff Spring Trail. I prefer to take this loop counter clockwise as stated above. On warmer days you get a shady return down Peralta Canyon. If you go clockwise and first head out on the Peralta Trail... you will encounter a minor ascent on the north end of the Terrapin Trail.
The trail on the south end of Black Top Mesa used to be called Needle Cutoff Trail. Now it's just a section of the Dutchman Trail. Old topographical maps are incorrect near the Peralta / Dutchman junction. The trail on the old topos appears to cut straight down and back up East Boulder Canyon (this canyon runs between Black Top Mesa & Palomino Mtn) Now the trail takes a more gentle approach. It zig zags down and back up so it's not as strenuous.
A couple things to think about... The first is on the Bluff Springs Trail. You want to take a right on the flat slab of rock in the creek. Get a topographical map; otherwise you'll end up heading up Barks Canyon. Next... you might be thinking of cutting this trip short with a crossover immediately north or even shorter immediately south of Weavers Needle. Fritzski wrote up some clues to the south shortcut. For the north approach get a topo and think Terrapin Pass. Beware, off trail adventures in the area can be hellish.
Check out the individual trails for further information: Bluff Spring Loop & Weaver's View, Terrapin Trail & Peralta Trail