Hi danestock,
The first place to start your research is the mattress shopping tutorial here (there is a longer version and a shorter version at the end) which has all the basic information, steps, and guidelines that can help you make the best possible choice … and more importantly know how and why to avoid the worst ones.
I would be very cautious about mattresses that are in lower budget ranges because people that are in much higher weight ranges will need more durable materials (which are generally more costly) and in many cases the quality and durability of the materials of the mattresses in your budget range may not be suitable for your weight. Many low end mattresses may only last you months before they start to soften, break down and start to sag prematurely under higher weight body weights and you may cross the thresholds from sleeping well on a mattress to sleeping “OK” to tolerating a mattress to finally deciding to replace it much too quickly relative to the price you paid even in lower budget mattresses. In some cases if the mattress is already on the edge of being too soft for a particular person in terms of PPP (Posture and alignment, Pressure relief, and Personal preferences) when it is new then even the initial break in period (usually from 30 - 90 days) may take you over the edge of the comfort/support range that would be suitable for you (see post #2 here) even though this is more of a suitability issue (choosing a mattress that is too soft) than a durability issue.
There is more about the most important parts of the “value” of a mattress purchase in post #13 here that can help you make more meaningful comparisons between the different mattresses you are considering.
There is also more information in post #3 here and the posts it links to that can help those that are in higher weight ranges choose a mattress that is suitable for their body type and weight range.
Some of the better lower budget online options I’m aware of are listed in post #4 here and in posts #3 and #4 here.
If you let me know your city or zip code I’d also be happy to let you know about the better local options or possibilities I’m aware of.
You can see some comments about the Brentwood Mattress in posts #31 and #32 here and the rest of the topic as well and as you can see either the shipping weight is very wrong or the specs they provide are completely wrong. Either way though … it uses 3" of 3 lb memory foam which I would consider to be a weak link in the mattress and I would avoid lower density memory foam completely … especially in your weight range.
The Tuft & Needle isn’t a memory foam mattress and you can see the details of the materials they use in posts #2 and #6 here). While their base layer is a little lower density than I would generally suggest in your weight range (I would generally suggest 2 lb polyfoam for your weight), it has much more durable comfort layers which are generally the weakest link of a mattress and would be a more durable choice than the Brentwood and the slightly lower density support core may be a good budget compromise because it’s more difficult to find a mattress that uses the most durable materials in your budget range.
Phoenix