Well, first, Starship has two winglets in the front and two in the rear, so depending on how those are deployed, they can dynamically adjust the center of pressure while in the bellyflop position. I imagine if it's running with a large payload, the forward fins would be more fully extended and the rear fins would be more folded back.
But that said, just because they can land with 150 tons aboard, doesn't mean they can land with any arbitrary object of that mass. I think there are certainly going to be limits about how the mass is allowed to be distributed to stay within the flight envelope.
The cargo adapter inside the Starship is pretty close to the center of the ship, just forward of the methane tank, so most payloads will sit well back from the nose. Only a pretty long piece of equipment would extend out towards the nose, and in that case it's unlikely to have a lot of weight up that far.
For a number of reasons, the connection point on a payload is usually going to be as near to the center of mass as is practical. You want to minimize the lever arm your cargo presents, since a long lever arm means the cargo effectively "weighs" more as far as the connector is concerned, and for all the structural elements between those points. For example, imagine tying a weight to one end of a ruler and then carrying the ruler straight out in front of you by the heavy end versus the light end. Your hand is the docking adapter, and you can easily see how much more strength is needed if the weight is way out there, if it's even possible to hold at all. And if you replace the ruler with thin cardboard, the cardboard can easily support its own weight when you hold the heavy part, but it would fold and collapse if you tried to hold it the other way.