Would be best if you start with an overall picture.

Existing slate patio with addition of slate added years ago. I would like to extend from the white pebbles until the far stone wall. The hill that the stone wall is holding back will be dug out as well. I dislike the slate due to weeds growing in between. I am also looking to save cost wise on extending the patio out 30x30. I was thinking a cement slab with gravel so that it doesn't look just like cement for the additional patio and in the future redo existing slate the same way?

Looking to raise the lower walls to match the existing patio height.

Existing slate patio with addition of slate added years ago. I would like to extend from the white pebbles until the far stone wall. The hill that the stone wall is holding back will be dug out as well. I dislike the slate due to weeds growing in between. I am also looking to save cost wise on extending the patio out 30x30. I was thinking a cement slab with gravel so that it doesn't look just like cement for the additional patio and in the future redo existing slate the same way?

Looking to raise the lower walls to match the existing patio height.

I can't grasp your question from your description. Scratching my head wondering how you mean to combine "cement and gravel." You say extend patio "from white pebbles to far stone wall" ... but I only see one wall. If the only reason to dislike slate is weeds, there are chemical solutions.

Let me clear it up. The stone wall to the right that is holding back the hill will be dug out and a new wall will be built to eliminate the hill and eliminate the curve. This wall will be built with interlocking stones.

This photo might show it easier the existing patio will be expanded to the end of the stone wall to your right hand side.

I am debating on continuing the slate or use concrete which is more level without any gaps which I would need to use chemicals to eliminate the weeds in between. Or another type of medium for a patio.

Here is the front view the wall to your right will continue on the left hand side which is lower to hold and expand the new patio. The stone from the wall holding up the hill in the back will be used to continue this wall.

Is this a project which you are designing yourself? If so, I would suggest that you hire a professional designer to help work through the questions you are presenting here. And to give a cohesive design theme to the finished product. (I still don't quite understand what you're asking. If it's just about what material to use, it's a question of cost & benefits. If you don't like the slate, you'll look at some of the other materials; plain concrete is not the only thing. I still don't understand: "...I was thinking a cement slab with gravel so that it doesn't look just like cement." ... the white gravel shown in the picture is the least attractive of what can be seen. Hope you don't use any of that in the scheme. The pictures you've provided are a lot of shots from all angles so it's hard for someone on this end to get a feel for the overall space. It is better when pictures are taken from one viewpoint and span the overall view continuously (slightly overlapping) from one end to the other so that all can be seen and the complete view "assembled" in the viewer's mind.

Be careful not to get the wall or patio too close to the trees.

Does this explain it better the purple area will be the new patio expansion. The red line is where the rock wall will be rebuilt to eliminate the hill and further expanding the patio. My question is should I continue using slate to expand or what are other alternatives budget friendly material can I use for the expanded patio area?

Here shows a longer patio view of Red where the new rock wall will be pushed back and built eliminating the hill and expanding the patio. The Blue will be continuation of slate. Should I continue using the slate to expand or what budget friendly alternative if I decide to eliminate all slate and use a new medium for entire patio? I hope this clears things up.

Probably means concrete aggregate...which I think would look good.

yes concrete aggregate. Sorry I didn't know the name. DO you think that is cheaper cost wise compared to continuing slate?

Use slate for the new patio area. I am concerned over all the soil you will be disturbing. Please ask a pro before you start to dig.

It looks like you intend to get very close to the large trees. I'd reconsider that.

Concrete will be the cheapest. There are many variables. It's best to come up with a plan, then ask the contractor how much the difference will be between various materials.