My solution is to make them neither fixed strength nor stat boosting. Instead they grant a Might die, plus something fun as well.
Might Die: A might die adds to Strength attribute checks, saving throws, and weapon attacks made using strength. If you have more than one Might die, you can roll them all and pick the highest.
If you have a Might Die, your carrying capacity is multiplied by the largest value of the might die.
Note that these do not add to accuracy. This is intentional; I like my accuracy to be bounded.
Example items using Might dice:
Guantlets of Ogre Power: (Uncommon, requires Attunement)
Grants a 1d4 Might die. In addition, you can wield two handed melee weapons in one hand; if you do so, they lose the HEAVY property.
Belt of Hill Giant Strength: (Rare, requires Attunement)
Grants a 1d6 Might die. In addition, as an action you can throw a boulder with 40/80 range of up to 10 lbs. It acts as a thrown weapon that deals 1d8 bludgeoning damage for every 5 lbs of weight (max 2d8 (9)).
Belt of Stone Giant Strength: (Very Rare, requires Attunement)
Grants a 1d8 Might die. You can cast Mold Earth at-will and Stone Shape as a ritual. In addition, as an action you can throw a boulder with 60/120 range of up to 20 lbs. It acts as a thrown weapon that deals 1d12 bludgeoning damage for every 5 lbs of weight (max 4d12 (26)).
Belt of Frost Giant Strength: (Very Rare, requires Attunement)
Grants a 1d8 Might die and you gain resistance to Fire and immunity to Cold damage. In addition, as an action you can throw a boulder with 40/80 range of up to 15 lbs. It acts as a thrown weapon that deals 1d8 bludgeoning and 1d4 cold damage for every 5 lbs of weight (max 3d8 (13)+3d4 (7))
Belt of Fire Giant Strength: (Very Rare, requires Attunement)
Grants a 1d8 Might die and you gain immunity to Fire damage. When hit by a melee attack or grappled, you can cast Hellish Rebuke; once you have done so, you cannot do so again until the next noon. In addition, as an action you can throw a boulder with 40/80 range of up to 15 lbs. It acts as a thrown weapon that deals 1d8 bludgeoning and 1d4 fire damage for every 5 lbs of weight (max 3d8 (13)+3d4 (7)).
Belt of Cloud Giant Strength: (Legendary, requires Attunement)
Grants a 1d10 Might die. You can cast invisibility, feather fall, misty step, fog cloud, and levitation on yourself; once you have cast each, you cannot cast that one again until the next noon. In addition, as an action you can throw a boulder with 40/80 range of up to 20 lbs. It acts as a thrown weapon that deals 1d10 bludgeoning damage for every 5 lbs of weight (max 4d10 (22)).
Belt of Storm Giant Strength: (Legendary, requires Attunement)
Grants a 1d12 Might die and you gain immunity to lightning damage and resistance to thunder damage. In addition, you can create and throw a lightning bolt as an action. The bolts act as a thrown weapon with 50/100 range and deals 3d12 lightning damage. The lightning bolts dissipate at the end of the turn they leave your possession, or if you summon another bolt.
The "side ability" scales with the rarity of the item. You can make the Might die system work for other attributes.
Reflex die for Dex
Fortitude die for Con (it adds to rolls that heal you directly)
Lore die for Int, Oracle die for Wis, Glamour die for Cha (all add damage on attribute-based spells as well, at most once per target)
Add side benefits with higher rarities to taste. Make the item not just "Belt of Dexterity", but something else, then add another ability based on that flavour (like I did with the giant belts).
The giant bolders; you either need to truck a huge number of such boulders around, or you'll have a limited amount of ammo. They scale from 2d8 up to 4d10 damage (plus strength, plus might die), but they require an action to throw them (so no multiple attacks).
