I think it is OOO (from the FCOM install I did) that boosts the penalties for wearing heavy armor (at least at master level). What is the simplest way for me to change that? Is it an .ini value or is there a mod I could use to overwrite OOO for those particular settings?

To reply to myself, I launched the CS and created a new .esp where I just went a modified the fMoveWightMax value to 200. I think that will basically reduce my "worn weight" effect on runspeed. Am I correct in this?

Also a question - any value I DO NOT modify in there (no little * sign next to it) are basically not being looked at right? Some of the values there are not even the vanilla oblivion ones. Kinda worried about that. If fMoveWeightMax is the only value with a * - that will be the only value modified. Right?

The star means that the value has been edited by the mod you have as the active file. I looked through the OOO pdf manual, but it just says that OOO does edit the values. TESNexus probably has a tweak or cheat mod for FCOM.
The FCOM release thread might have a link to a Wiki site, or a "spoilers" thread, use the link in my signature to check.
When I do edit something like this, I just copy the values directly from Oblivion.esm. I would esmify the OOO esp, select Oblivion.esm and the esmified OOO esp with check marks in the CS, and create a new esp that edits OOO.
I place the new esp directly after the OOO esp in my Load Order, rebuild my Bashed Patch and see if it works. Remember to espify the OOO esp after you make the patch and before you rebuild your Bashed Patch.
EDITED for wording. Using this method also means you can just delete the new esp if it does not work, and avoid the hassle of reinstalling two or three different mods if you use OBMM.

OOO doesn't edit fMoveWeightMax. In fact, checking in TES4Edit none of my FCOM mods does, so should perhaps be Fran's (which I don't use) or an optional combat settings plugin? Speaking of TES4Edit, it's very much recommended as you can see which mod that affect exactly what in a given load order. So loading it and checking fMoveWeightMax in Oblivion.esm will point out the culprit.

Anyway, http://cs.elderscrolls.com/constwiki/index.php/Movement_Game_Settingst I was going to say that I think you're looking for

fPerkHeavyArmorExpertSpeedMult
fPerkHeavyArmorMasterSpeedMult

but none of them are changed by OOO when checking in TES4Edit either. In short, not sure what/which mod affects it.

OOO 1.3's description says it removed the Master PERK of Heavy Armor so that there is always a speed penalty even at Master level. But if the values you listed are not touched I'm not sure how they did it.

I basically just want Heavy Armor's speed penalty to be reduced across the board. I want to move slightly faster without touching fMoveRunMult. I also want to keep the fact that running in light armor lets you go faster still. Speeding movement globally would usually be done with fMoveRunMult but I think modifying WeightMax or the athletics multiplier values will have the same effect. If anyone could confirm that would be helpful.