If your symptoms tend to go away after you get up and move around for a while or if you find you sleep “symptom free” on other mattresses that you have slept on then the most likely cause is your mattress. If your symptoms tend to remain throughout the day or if you have similar symptoms on other mattresses then the most likely cause is your back. Of course it could also be a combination of both.
At your weight you certainly wouldn’t “need” 12" of latex (you’re right that it can be more important or “necessary” in the higher 200 lb weight range and above) but you may still prefer it. Some people may feel very little to no difference between them while other would notice a more significant difference (higher weights would probably notice a bigger difference than lower weights). There is more about the effect of thickness and the benefits of having more layers in post #14 here.
There is also more in post #2 here about the different ways to choose a mattress (either locally or online) that can help you identify and minimize the risks involved but when you can’t test a mattress in person then the most reliable source of guidance about your comfort choices will always be a more detailed conversation with a knowledgeable and experienced online retailer or manufacturer who will know more about “matching” their own mattresses to different body types and sleeping styles than anyone else.