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Source: NASA via wikimedia.org
As the image shows, in multiple parachutes, each assumes a position away from the center. The post, Why don't 3-parachute descent systems collide and collapse?, says it's the air spilling from each that ensures separation (non-vertical alignment).
In the zoom and crop below, there seems to be an offset dark feature on each parachute:
What is that? (The photo is the Apollo 16 landing.)
Those dark objects are the deployment bags which contained the main parachutes prior to inflation.
Source: The Apollo Parachute Landing System
Also from Apollo 15 Main Parachute Failure Anomaly Report
Two 16.5-foot diameter conical ribbon~type drogue parachutes are mortar-deployed 1.6 seconds after forward heat shield jettison. The drogue parachutes are deployed in a reefed condition and, 1O seconds later, inflate to the fully open configuration. The drogue parachutes are released from the command module at an altitude of about 11000 feet. At drogue parachute disconnect three 7.2-foot diameter ring-slot pilot parachutes are mortar-deployed. The pilot parachutes provide the force necessary to release the main parachute retention system and pull the main parachute pack assemblies from the upper deck. As the main parachute packs are pulled away from the command module, the parachutes are extracted from their deployment bags. Each main parachute inflates through two reefing stages to the fully open configuration.
(emphasis mine)
I cropped and annotated this Apollo 16 image to show the entire system: pilot chutes, deployment bags, and main canopies.
Red arrows - pilot chutes; Green arrows, deployment bags.
There are no "weights" provided on top of the parachute canopies.
