What is the best healing item to use at tier 6 and tier 7?

It depends.

Outside of battle, there's the Healer.

In battle, it depends a bit on the challenger you're facing, your budget and the rest of your weapon set. A once per battle healer which will be usefull throughout all tiers is the which heals for 100% of your hp. Then there's the which is also a once-per-battle item and heals for 90%hp. Usually the Phoenix Quill alone is enough though.

The is a T7 weapon which heals a flat 100hp and is not classified as a healer, so it can be combined with other healers in your set. The is a T7 weapon that heals 7% of your hp and is not classified as a healer. I'm a bit out of the loop for this one, since it's a scaling weapon, and I'm not quite sure how it scales, so you'd have to look into that. The is the T6 king of healers. It heals for 10%. I don't have one myself, but I think it's probably classified as a healer, which means you can't use another "healer" weapon in the same set. This one can be pretty usefull for several tiers.

There's infinite use scrolls and once per battle scrolls. It's nice to have a mix of both. If you take at least one infinite use scroll into battle, you'll always have some healing in a turn, although the once per battle scrolls are able to heal a lot more in a single turn. Scrolls depend largely on your budget and the intelligence of your pet, since they're not limited by tier. There's a really nice scroll guide here. I'd try to go for either a or paired with a couple of once per battle healing scrolls like . would be better, but at T7 they're kinda pricy, probably overkill with the healing, and you'll be able to win your own later on.

There's also pylonics, I always forget about them :D The heals 100 hp, but it's single use, so it'll be consumed when you use it.