Its something me and my girlfriend discovered while playing, since a Rune Knight's "Giant's Might" might can be used to increase your size from medium to large, and enlarge/reduce can then be used to double that size up again. It's really fun for RP moments of threatening enemies into surrendering as my Fire Genasi suddenly grows four times his original size, but beyond that my DM is still a little confused as to what increasing to such size would actually mean in raw mechanics.

As far as I understand it simply means I have a strenght adventage and deal and extra 1d4+1d6 melee damage with my weapons from Giant's Might and Enlarge respectively, not to mention now taking up 15 by 15ft in space. 

Does anything beyond that happen though? I honestly don't know.

You have more reach, and can reach more things now that you're larger. You can opportunity attack more things when you have more space touching others spaces. Other than that, I'm not sure

As written, very little changes aside from what you have stated. I don't think it even gives you reach unless it says so like the level 18 Rune Knight feature does (I would grant a 5 foot increase in reach for a creature that increases two sizes, but it would be a houserule). Keep in mind the extra 1d6 is only once a turn (an incredibly lame and reality-twisting restriction they added IMO - is your weapon only bigger for one attack then it shrinks back down?), but the 1d4 is always on.

Your weight increases massively, which can have an effect ranging from zero to super important depending on your DM and your surroundings. I wouldn't try it on a frozen lake. But overall I agree with you that it's pretty anticlimactic from a mechanical standpoint. That doesn't stop me from casting Enlarge on he druid in bear form though. Sometimes you have to be satisfied with the cool factor.