I used to have no problem starting this game but now suddenly it opens in a tiny box and does not resize to fit my screen. Anything I can do about that?

There are FIVE Heroes of Might & Magic titles on GOG alone, plus Heroes Chronicles as a sixth product. WHICH game is "this"?

Keep Aspect ratio - as mandatory option set on everywhere possibke. Video drivers, display OSD/app settings, ingame, ingame wrappers or 3rd party one. Or like for GOG HOMM1+2 releases - in DosBox config.
In every of settings set Keep ratio, integer scaling and forcing chechbox'es if any such additional ✅ present.

For DosBox there is output specific options. And windowed/fullscreen switcher by General Windows (all of Win OS family) hotkey - Alt+Enter. Need exact title for that. Or just look to DosBox documentation on PCGW and official website.
GOG and GOG Galaxy are differ build and Galaxy is additional specific troubleshoot (galaxy need to be in games folder too and admin run in some cases to apply admin mode to games started directly).
For GOG (offline) builds there is still differ alternates. Heroes 3 4 5 Chronicles come as one offline and one online build. Heroes 1 fome as two offline builds - DoxBox and virtual disc image inside as alternative. Heroes 2 same and additional windows-build installer. So it is 3 and 4 build for H1-2.

For Heroes 3 and above it is sysytem settings change or ingame (win registry for Heroes34 and My Documnts for H5/tote). While for H1-2 most likely DosBox settings rated.
Tribes of the East is separate game as well. Not a Heroes 5 entirely differ game. So need to clearly state you have TotE issue if it is.

If you have changed settings and you sure it was not from system/video driver settings changing recently - this is somehow related to OS wont allow to load previous ingame/dosbox settings.
Make sure games installed strictly to X/Games/.Galaxy too.