Hi tlab.
Welcome to our Mattress Forum. 
It’s hard to give a specific recommendation (like “you should sleep on X brand”) because ultimately what every person feels on a mattress is different and only you’ll know what is supportive and comfortable for you.
Is your current medium bed not feeling supportive to you at this time? Are you looking for something similar in feel? Something softer? Firmer?
With higher BMIs and a likely weight differential between you and your partner, the Mattress Durability Guidelines will be especially important.
Mattresses with coils are both comfortable and supportive for heavier sleepers, and many will say they find them more durable than beds constructed solely out of foam. This, again, comes down to making sure you choose the appropriate materials and overall thickness for your sleeping profiles and BMIs.
There are also a number of forum posts and threads about mattresses and higher weights and a forum title search on heavy (you can just click this) will bring up many of them. Some examples include post #2 here and post #2 here and this thread.
If you and your girlfriend have fairly different needs with regards to support and comfort on a mattress you may be interested in checking out split configurations.
I would suggest checking these options out (split bed or not)…
Arizona Premium
Sleep EZ
FloBeds
Nest Bedding
I look forward to hearing more about what it is you are looking for in a mattress.
NikkiTMU