"Select Through" with Tweak Tool?

Although I have X-Ray on, when manipulating vertices in a line in an orthogonal view, only one vertex at a time is affected. I’d (much) prefer that all vertices in line with the view be affected by the tool.

Is there a way to make that happen? If I have to select with the Box tool it doubles (at least) the number of clicks and/or hotkey presses, so is quite inefficient.

So, it sounds like you want Blender to smartly select multiple overlapping vertices in a single click. So, the short answer is that Blender’s default selection without any additional tools or modifier keys doesn’t work that way. One click equals one item selected. Imagine if Blender routinely selected more than one item when you clicked on it. There would be a lot of deselecting. You may need to adjust your workflow.

I learned Blender with my left hand on the keyboard and my right hand on the mouse. That makes it easier than choosing different tools with the mouse and fumbling through a tool list. If I want to select vertices that are in a vertical line, horizontal line, square group, or rectangle group, I press “B” for Box Select. If I want either a circle or I want to "paint"my selection, I press “C” for Circle Select. If I want to draw a non-square, non-circle, arbitrary continuous loop around a set of vertices, I hold Ctrl and use RMB to do a lasso select. All of those tools will select everything that is visible (just know whether you intended to have x-ray turned on or not).

A lot of the conventions have been thought through, but some of them just require a change of thinking on the user’s part (e.g., right-click select).