I use Windows 7 Home Premium 64-bit and Steam version of the game, with virtual memory (swap file, if I understand you correctly) disabled. I run the game as administrator, same as you. The game starts one process, not two, checked this several times. When I tried to launch it in fullscreen mode, it often started minimized and didn't opened the window, this was resolved by setting the video mode to pseudo-fullscreen. I even tried to update the video drivers (and my Windows Aero interface now rests in peace).
With no swap file, your system has no way to keep more than 16 GB, and if I check how much is reserved once I load a game in BG3, I see that about 15 GB are already used.
That's just when starting after a fresh reboot of the system. I'm usually trying to keep it clean (thankfully it's easier with Windows 7 than Windows 10), so there's mainly an antivirus, nVidia's drivers and Chrome running (and what the OS is using). I can imagine that after a while, if there's a memory leak in their code (likely at this stage since they seem to use C++) or if it's poorly managed, the required memory will increase over time.
I'd try to set at least 8 GB of swap file and see if that solves the problem
You seem to know your system, but just in case: System (Win+SysRq key), Advanced system settings, Advanced tab, Performance/Settings, Advanced, Virtual memory.
You can select on which drive it will be stored. If it's on your HDD, I'd recommend using the same value for 'Initial size' and 'Maximum size', so that the swap file doesn't change size all the time, which leads to disk fragmentation and degraded performances. If it's on an SSD, it's less important.
