Why such low voltage across my filtered half-wave rectifier?
Your signal generator's output impedance is non-zero. It's probably at least 50Ω, but could be much higher. It cannot source very much current (in fact, trying to source a whole lot of current may make it very unhappy).

Add some series resistance to your LTSpice simulation's voltage source, and you'll see a graph that matches what you have on the scope.

Also, not entirely on topic, but your schematic has 10F and 33F capacitors in it, which at 60V would probably about the size of my head. I'm guessing those are supposed to be uF. Notation is important. Additionally, in LTSpice, you can use suffixes like Meg, k, m, u, n, p for units, which makes things much more readable.

Edit: neatly enough, if you put that circuit into LTSpice, and change the source impedance to 50Ω, it matches exactly to your scope traces! So everything is right in the world: you've got a signal generator with a 50Ω output impedance, and your simulation matches the real world exactly. Pretty rare, that.