Hi dsw61,
There are really two parts to your question.
The first part involves the pros and cons of having two 3" bottom layers (such as 3" + 3" + 3") vs a similar mattress that is the same overall thickness that uses a single 6" base layer (such as 6" + 3") and there is more about the pros and cons of each in post #2 here.
The second part of your question involves the pros and cons of a thicker mattress such as a 6" + 3" + 3" (12" total) mattress vs a thinner mattress such as 3" +3" + 3" (9" total mattress). In this case the thickness of a mattress or the number of layers or the thickness of any individual layers inside it is really just a side effect of the design and the design goals of a mattress and the thickness of any individual layers or the complete mattress is also only one of many variables that can affect the feel and performance of a mattress relative to any particular person (see post #2 here) and by itself isn’t particularly meaningful (see post #2 here). In some cases higher weight ranges (or a higher BMI) will sometimes do better with a mattress that is thicker than lower weight ranges or a lower BMI (see post #14 here for more about the effect of thickness) but even this depends more on the specific design and combination of materials in the mattress and on how well your testing or personal experience indicates the mattress “as a whole” matches your specific needs and preferences in terms of comfort, firmness, and PPP than it does on just the thickness itself.
When you can’t test a mattress in person then the most reliable source of guidance is always a more detailed phone conversation with a knowledgeable and experienced retailer or manufacturer that has your best interests at heart and who can help “talk you through” the specifics of their mattresses and the properties and “feel” of the materials they are using (fast or slow response, resilience, firmness etc) and the options they have available that may be the best “match” for you based on the information you provide them, any local testing you have done or mattresses you have slept on and liked or other mattresses you are considering that they are familiar with, and the “averages” of other customers that are similar to you. They will know more about “matching” their specific mattress designs and firmness levels to different body types, sleeping positions, and preferences (or to other mattresses that they are familiar with) than anyone else.
Phoenix