Welcome to the Mattress Forum!
Congratulations on your new mattress! :cheer:
You’re not providing any meaningful details about the mattresses you chose (11” and 13” don’t provide much information that is usable, as Brentwood Home makes many different mattresses), so I can’t provide any meaningful information about the product you chose or are considering.
Otm_shank did make some good points that you’d want to consider. In order to make an informed decision about switching to a different mattress, you need to find out the information listed here so you can compare the quality of the materials and components to the durability guidelines here to make sure there are no lower quality materials or weak links in a mattress that would be a cause for concern relative to the durability and useful life of a mattress before making any purchase.
Having a high BMI presents special challenges and generally requires firmer materials (in the support layers especially). This could be firmer latex or innersprings (the type of support component would be a personal preference and in the right design either could be suitable) or even a zoned construction. The same overall guidelines apply with higher weights though that PPP (Posture and alignment, Pressure relief, and Personal preferences) along with using high quality durable materials that will maintain their feel and performance for longer periods of time are the way to make the best choices. Heavier people in general will need firmer and thicker comfort layers and firmer support layers than those who are lighter and because no materials will last as long with much higher weights the quality and durability of the materials and components is even more important than normal. I wouldn’t “rule out” any types of mattress and base your choices on your own personal testing. Post #3 here has more information and suggestions about heavier weights that is worth reading.
Higher BMI ranges will need more durable materials and components in a mattress and in a BMI range of 30 or higher I would include any 1.8 lb polyfoam or 4 lb memory foam as a “lower quality/density” material (relative to a higher BMI only) and minimize their use to a total of “about an inch or so or less” in the mattress.
Polyurethane foam: If your mattress is one sided then I would look for 2.0 lb per cubic foot density or higher. If the mattress is two sided then I would use a minimum density of 1.8 lbs per cubic foot or higher.
Memory foam (or gel memory foam): If your mattress is one sided then I would make sure that any memory foam is at least 5 lb per cubic foot. If the mattress is two sided then I would use a minimum density of 4 lbs per cubic foot.
If the materials were the same in the two mattresses you are comparing, with just less of the material in the thinner mattress, then the thinner mattress would generally feel softer for someone who has a higher BMI. But without knowing the materials of each mattress (the 13” and the 11” you mentioned) and their densities, I unfortunately wouldn’t be able to provide much more meaningful information for you.
If you are able to provide more detail, I can do my best to be assistive. You may also wish to place a phone call to Brentwood Home and ask them their opinion, as they would be best suited to provide a detailed answer and advice, being most familiar with the products they offer.