I use this:

You can get it in a long handled version as well. That long forked tongue is perfect to go deep along the root and then pry it up. Is intended for dandelions but works great on any deep rooted or well established weed and in close quarters. Between this and my 3 prong cultivator, I am set!!

I love my root slayer. You can find it on Amazon, at Ace, Lowe’s, Gardeners.com and other places. The one I have is somewhat heavy, but the weight helps with the digging. I have heard there’s a lightweight version and also what looks like a shorter handheld version. I wouldn’t be without it.

debra

The Rogue Hoe. Small head, to get in tight places. Sharp on 3 edges. Quality steel that holds an edge well. I think they come in a couple of different head sizes and handle lengths.

Local garden reporter recommends " cobra headed weeder"

I use a knife life tool from A M Leonard. It digs out everything from shallow weeds to deeper and thicker roots.

I use a three-tool kit consisting of:

A cheap japanese hand hoe for shallow-rooted things like creeping charlie and chickweed

A Nisaku hori-hori for deep-rooted things like dandelion and thistle

A Rogue wide scuffle-hoe for large patches of nonsense* (see wintercreeper).

I add one of those Fiskars three-tined dandelion pullers for lawn duty, but frankly, I think I have given up with that task.

Thank you much for help, love ideas! 

Starting my vacation planting garden. Bought several tools from your suggestions. We will see. It is cold here again.