Been backpacking for decades and have been entertaining the idea of ultralight. Met a guy years ago whose pack weighed 12-15lbs but wasn't interested in leaning his secrets at the time.... Now I am. I am 46 y/o and looking for new challenges so ultralight has come up as something I would like to dive into. Since I live in the Deep South, tarp shelters are not practical except during the dead if winter due to our insane mosquito infestation, so I have purchased a jungle hammock with mosquito netting. Now I need advice on EVERYTHING else. Bedding, pack, equipment, etc.. I should have cooking down since I already use mini stoves and/or esbit stoves.
   All advice would be appreciated. No detail too small. I would like to also know what size sil/nylon tarp to get. I am thinkng 10x10.

for tropical weather / wet season I used the gi jungle hammock for long term camping...so it wasnt really ultralight travel utilization...but here ya go:

I used old tent poles to place in the roof corners at each end of the hammock,
I pushed stronger sticks (or 1" dowel) into each canvas loop of the hammock on either end to keep the hammock from bunching up on me like a cocoon.
I tied little pieces of string on the main ropes to draw water away from running downward towards the canvas
inflatable sleeping pad fit right into the hammock perfectly
after sleeping; just flipping the whole hammock upside down would give you good daytime hammock plus handy storage area
I had about a 20x12 nylon fly from campmor for overhead protection and side wall.
msr XGK shaker multi fuel stove
katadin water filter

good luck....many nights I would wake up with knees sore from hyperextension in the hammock...

oh yeah...I think the sleeping pad was acquired because those little bastards would bite right through the canvas

Depends on the temps and precipitation.  You might want an underquilt and overquilt combo.  Down is usually preferred since it can compress better than synthetic insulation.  You can also use a sleeping bag and pad in the hammock, if you don't want to go with the quilts.  As for tarps.  You can go pretty simple or go all out.  It depends on your desires and budget.  A simple sil-nylon 10x10 will be perfectly usable.  It's recommended to have it hang 1/2 to 1 ft past the edge of your hammock for rain situations.  Also, you can add a piece of cord larks headed over the main suspension to block water running down the rope and into your hammock.

I was pretty big into it, and you can go really light with hammocks (with expensive gear) but it is tricky to get that ultralight zone with them.

My entire winter set up at one point was about 5 lbs for everything, but I had close to $1000 invested.

Summer was easy though, with a down underquilt and a poncho liner for the top I could do an entire shelter and sleep system for under 3 lbs and be the most comfortable guy in the woods.

I went back to ground, a sub 2 pound tarp is a palace and I just need to scale up from there for insulation for the season.

Remember too that ultralight sacrifices a lot in the name of moving faster. You have just what you need to get where you need and literally nothing extra. It isn't my thing really, but I do like to as light as possible while still being able to stay self reliant if I need to stay out longer than I plan.

Also (shameless plug) I have a Hennessy Hex tarp for sale in the EE for cheap if you are interested. 12' ridgeline, easily covers most hammocks.

Things we have changed to trim weight:
Leatherman turned into Victorinox knife (only fear is needing the pliers if the knob breaks off my stove)
GPS went away (spare AAs with it)
Cooking way less (fewer utensils, fewer vessels, smaller gas cans)
Wife got a modern backpacking rain jacket (I haven't yet but I wish I had, this may be the largest item you can change)