There are many, many vibrato bridge designs where the arm screws down deep beyond the base plate and into the block.
There is a very, very, very useful modification to these - take the arm (at least!) down to your good full-service creaky dusty ol' hardware store - hopefully the entire guitar. NOT the bright shiny ACE chain hardware store with vacuum-wrapped "product." In the back you will find spools of white plastic polyethylene tubing. Not clear fish tank tubing, this is translucent and stiffer. You will find a piece that snuggies up over the threaded portion of the bar but slips partway into the top hole of the bridge. The original design of these things are horrid - the threads are way at the bottom, which creates a lot of leverage and if they're screwing into potmetal zinc... well where did YOU think those tiny metal shavings were coming from, THE GEARS IN YOUR BRAIN?!?! :icon_scratch:
What the tubing does is transfer a lot of the stress to the interaction between the upper, non-threaded part of the bar and the upper non-threaded hole. If you just can't find a real hardware store anywhere, you have to find some other... well, 'zampily, the really skinny Papermate ballpoint disposable pens have a section of the shaft towards the tail that'll do. They're such godawful writing devices you're actually liberating the poor downtrodden pen's ass into a world of creativity and joyful music!
There's another pen part that does it, I think it's part of the cartridge of Pilot G2's? Saving old dead pens of various ilk is a good way to start upping your plastic cylinder collection, as they say in the fountain-pen repair biz, "You're only as good as your junk drawer"... in desperation & despair, some have even resorted to wrapping nylon plumber's tape or even duck tape around that little top 5/8" of the bar, which eventually results in a gooey mess of destroyed tape, but better that than a destroyed tremolo.
Regarding the issue of adding weight or "mojo" to the spring-suspended area, it may be instructive that one of the leading purveyors of brass blocks for the obviously "weighty" sounds - "Tired of that old crappy lightweight block stifling your creativity to the point that all the other guys laugh at you, kick sand on you and steal your chick?" - is also one of the leading purveyors of ultra-lightweight titanium blocks - "Tired of that old crappy brass block weighing down your seething talent which is just about to BURST as soon as you get a... lighter block?" I think objectively, you have to calculate the wavelength of musical vibrations, expressed as a factor of the variant vibration speeds of the molecules of different metals? Or maybe it's the molecular speed that's the factor and the notes are the... factorees? Do let us know how it comes out.