I have a Shimano Calcutta 51, that's small for a round reel, but it's at 7oz. Also have a Shimano Curado 51E, very low profile but weight 6.9oz. Both are very easy to hold and palm.

 

I know there are reels under 6oz but are they also small in hand reels?

Was getting ready to ask if you meant small or light until I read your last sentence.  Don't know if they are the smallest, but my Pixy Type R seems small to me.  There are lighter reels though.  Forget the first rod I tried it on, but the original Concept A reel amazed me at how small it felt when I first mounted it on a rod.  Reel seat may have had something to do with that.  Normally I never notice small details like that.

 

EDIT:  Maybe look at a Shimano Aldebaran MGL.  Never seen one, but I believe they are light and small from what I've read.  Smallest?  Don't know.

Sub 5 oz casting reels:

Daiwa Steez AIR TW 500XXH                 4.75 oz

Lew’s® Custom Lite SLP                        4.9 oz

Shimano 18 Aldebaran MGL 30HG        4.8 oz

Shimano 22 Aldebaran BFS XG              4.6 oz

 

All are small form-factor, low profille reels.  Highly recommended.

What’s the weight of the daiwa Tatula 70 SV?

Just now, Cbump said:

What’s the weight of the daiwa Tatula 70 SV?

6.5oz - https://daiwa.us/products/tatula-sv70

 

Heavier than my Patriarchs which are 6.3oz

Dang 

My team Lews hyper mag is super light. 

All the reels I listed are "small in hand" but they are lighter.  No downside except perhaps with respect to your budget constraints.

These are small and 4.8 ounces.

Revo mgx is tiny in hand and weighs 5.0 oz. The mg extreme is a fraction lighter.