Hi vpr,
Welcome to the Mattress Forum! … I’m glad you found us 
Just in case you haven’t read it yet … the first place I would start your research is the mattress shopping tutorial here which has all the basic information, steps, and guidelines you will need to make the best possible choices.
The questions you have really boil down to two categories.
The first one is the suitability of a mattress and for this you will need to do some testing on some local mattresses to decide which materials and types of mattresses you tend to prefer and which ones are the best match for both of you in terms of PPP (Posture and alignment, Pressure relief, and Personal preferences). This would be very helpful regardless of whether you decide to purchase locally or online since only you can decide on the types of mattresses and materials you tend to prefer and it will also help the online manufacturers/retailers you are considering to find the mattress that would have the best chance of success. I would also have a more detailed conversation on the phone with any online retailer you are considering because emails aren’t a great way to find out what you (and they) will need to know to help you make the best choices (see mattress firmness/comfort levels in post #2 here).
The next category of questions boils down to durability issues. When you are in a higher weight range then regardless of the types of mattresses or materials you tend to prefer it is more important to make sure that your mattress uses high quality and durable materials … especially in the comfort layers. There is more information about this in the links in the tutorial post and post #3 here and the other posts it links to also has more information that would be helpful for those that are in higher weight ranges. I would also keep in mind that firmer materials will feel softer to you than they will for your wife who is much lighter and will compress the mattress much less.
The two of you may also have very different needs and preferences so the first part of post #2 here has more information about how some mattresses can accommodate two people that are in very different weight ranges.
Once you have decided on the materials you prefer in your comfort and support layers (polyfoam, memory foam, latex, innersprings etc) then you will in a much better position to narrow down your choices.
In the case of both Tuft & Needle and Casper they both only have one mattress with one firmness level (although Tuft & Needle has two different thicknesses of basically the same mattress) so with both of these they would either work for you or they won’t. If they work everyone is happy. If they don’t they both have a good return and refund policy. The Tuft & Needle is a polyfoam mattress that uses 1.8 - 2 lb polyfoam which is a good quality material although it’s not as durable as more premium materials such as latex or higher density memory foam or polyfoam. The Casper mattress uses a combination of synthetic latex and 4 lb memory foam in the comfort layers over a 1.8 lb polyfoam support core. The synthetic latex would be a very durable material but I would normally minimize the use of 4 lb memory foam for higher weight ranges. In this case however the memory foam is only 1.5" thick so this wouldn’t be a major durability issue.
Post #4 here has more about Dreamfoam and Brooklyn Bedding who are sister companies. Again … regardless of which type of mattresses you prefer I would make sure that you use higher quality materials in both the comfort and support layers (I would lean towards 2 lb or higher polyfoam in the support layers at your weight) because more durable materials in all the layers are more important in higher weight ranges. They both offer a wide range of mattresses and many of their latex mattresses have layers that can be exchanged after a purchase if you need softer or firmer comfort layers. Many of their latex mattresses can can also be ordered with split comfort layers with a different firmness on each side if you order a king size. They also have a customizable 12 in 1 polyfoam mattress that uses 2 lb polyfoam which can be customized in many different ways after a purchase and can also be ordered in a split configuration in a king size.
After the suitability of a mattress and the durability of a mattress then the other parts of your personal value equation that are important to you would also be part of the “value” of a mattress purchase.
There is more about the many variables that can affect the sleeping temperature of a mattress in post #2 here and the posts it links to.
If you let me know your city or zip code I’d also be happy to let you know of the better options of possibilities I’m aware of in your area where you can do some testing on different materials and types of mattresses.
There’s a lot of information here but if you follow the steps in the tutorial post one at a time (with the addition of the optional online step) then you will have the best chance of finding your “ideal” mattress.
Phoenix