I had a thread similar to this a few weeks ago.

A lot of people said you can do both with some of the newer sets like wizards ripstoe.

What I ended up doing on my healer is running 5 heavy seducer which gives good recovery while still being very tanky.

I also run sword and shield for that extra blocking.

This is PVP btw, not sure how pve would work.

Wizard's riposte won't work in PvE since NPCs can't critically hit you,; it will never proc. I'll go with 1L/1M/1H or 2L/5H for the undaunted mettle passive, with tri-glyphs so you can have a bit of stamina for blocking. A good set combo would be 5 Armor of the Seducer + 5 Sanctuary or Spell Power Cure + 2 Engine Guardian or 2 Sentinel of Rakugamz. Heavy chest, legs, feet, head, shoulders, medium or light hands, light waist with infused on full enchant pieces and either sturdy or divines on the 40% enchant ones. 1H+S front bar, resto staff back bar. Shield play enchant on jewels and ~30 CP in shadow ward, either max health + max magicka or tri- stat food, atronach mundus.

Heavy armor gives more mitigation, especially physical mitigation, more HP. From my experience the lower limit for a tank is about 23K health. That's if you have a strong shield. I've tanked with a shield sorcerer and some things really hit hard. You can't heal an one shot trough block. Ex. vCoS is pretty brutal if you don't have strong mitigation.

Hybridizing is good if you want to run as a proper tank, but won't work well if you want to heal at the same time, since heals scale from your magicka pool and spell damage. That's why I was suggesting a full magicka attribute distribution, with the minimum of stamina gained only from tri-glyphs on armor and tri-stat food. With tri-glyphs and 4 infused full armor pieces (shield, chest, head, legs) you'll have about 13.5K stamina without putting any attribute points in it. Health should be about 22K, without any points in it, armor set bonuses and only food buffs. With tri-stat food you'll probably be around 16.5K stamina but only about 20.5K health. Magicka pools should be around 37K and 35K respectively, assuming you have racial bonuses that boost your maximum magicka. That's why I consider 5 Seducer's + 5 Sanctuary + 2 Sentinel of Rkugamz to be probably the best combo, since Sanctuary boosts health by 1K (1.15K next patch).

Seducer's adds 250 magicka recovery and 1K maximum magicka, and 8% cost reduction on the 5th piece - this is essential because you don't have much cost reduction from light armor, and healing is rather costly.
http://elderscrollsonline.wiki.fextralife.com/Armor+of+the+Seducer+Set

Sanctuary adds 1.1K health, 1K magicka and 4% healing taken, and 12% healing taken for you and your group within 10 m. The latter might not look like much but it boosts your heals quite a lot, since you will be lacking the spell damage and spell critical which you would have if you used light armor.
http://elderscrollsonline.wiki.fextralife.com/Sanctuary+Set

Sentinel of Rkugamz further boosts your heals by 2% from 1st piece and allows you to passively recover stamina for you or your group. It will proc quite a lot if you stack HoTs on your group, for example extended ritual, rapid regeneration and energy orbs. Using BoL should be very limited, due to the fact it's expensive even in light armor, let alone heavy, even with the cost reduction.
http://elderscrollsonline.wiki.fextralife.com/Sentinel+of+Rkugamz+Set

I would use the following bar setup:
Front Bar 1H+S:
Pierce Armor | Heroic Slash | Defensive Stance | Breath of Life | Harness Magicka || Reviving Barrier
Back Bar:Restoration Staff:
Inner Rage | Rapid Regeneration | Radiant Aura | Extended Ritual* | Channeled Focus || Aggressive Warhorn
*if the fight is mobile and resource intensive use energy orb or luminous shards instead