I estimate HC mode only adds 30lbs to you.

Carrying 5lbs each of water and food at a time should be plenty.
Carry ~20lbs of ammo for the weapons you are using, and stash the ammo that you aren't carrying the correct gun type for.
Throw in two medical bags for limb healing.

I have completed 1 hardcoe playthrough and I didn't notice a ton of change. Honestly, I didn't get a lot of issue from carrying the ammo. I tend to favor Melee/Unarmed when I can to save on it but there were times when I certainly felt like I was going through a ton of food and water. Thankfully I made enemies of Caesar's Legion so they kept me very well supplied with Purified Water and various fruits and veggies.

I sell frequently and don't carry much junk and inventory weight was NEVER an issue on hardcoe mode.