OK. I found Process > MIDI Fx > Cakewalk Fx > Velocity which brings up a silvery Velocity machine face popup. This shows a rivet in each corner and is mainly taken up by a dark red screen with settable variables headed
 
SET, CHANGE, SCALE, LIMIT, CHANGE, GRADUALLY, AMOUNT, TENDENCY. These are set at
 
100 -- 0 -- 1% -- 127 -- 120 -- 100% -- 1 -- 0. Below LIMIT, CHANGE and GRADUALLY are little boxes saying 1, 1 and 1%. Am I in the right place? There's no mention of min or max.   

I was referring to Process > Find/Change.

In order to use the plugin successfully you MUST make a note selection before opening it, otherwise any changes you make via the plugin will apply to ALL notes.
 
Brundlefly's solution above is a good one though it does force all selected notes to a single value.
 
The specific steps I would take are:
 
Select entire clip
Process > Scale Velocity
This should default to values of 100 in both boxes
As a starting point, set them both to 140, click Percentages, then Ok
 
Have a look at the velocities in the PRV. If it's not what you want, undo & try again with different values
 

Initially trying what you said, weak notes were still weak and faint on the screen. Volume knob is up. Trying different strategies in that popup brings results that refuse to show any logic. I can get it to play very softly or loudly this way (and variations there of I've been trying), whether changing Begin to 111 and End to 67, then vice versa or setting them both high or both low -- yes, checking Percentages (though I tried it without as well). 
 
Why can't there be a simple control for this within sight of the word Velocity? That's all I want to adjust. 
 
Find/Change does not show under Process, Brundlefly. 

Just noticed you are using S7. Back then, Process > Find/Change was Edit > Interpolate.
 
Note that 'Gain' on MIDI tracks is actually Velocity Offset. This can be used to quickly increase the Velocity of a whole clip by a fixed amount. But selectively adjusting just the lower limit is a special case that requres more steps.
 
 
 
 

It would be a very easy CAL program.    
 
Something like,
 
Get My_minimum_note_velocity
 
foreach Event where event type = NOTE if note.velocity < my_minimum then (= note.velocity  My_minimum). 
 
If you know anything at all about programming take a look at some of the samples provided in Cal Scripts, and modify. 

;;---  something like this should work.   You always have to make sure the parens balance. 
;;   Select notes however you like: the program will apply to all notes selected, whether by track, by range of time, or by
;; range of pitch, or some combination.
 
(do
  (int My_min 64)  ; default value
  (getInt My_min "Enter minimum velocity: 1 126 )
)
 
;; body
 
(do
  (if (== Event.Kind NOTE) (do
        (if (< Note.Vel My_min (= Note.Vel My_min)  )
       )
  )
) 

In Platinum, Ctrl-F1 should take you to the Cal scripts directory (At least on mine...)    Identify the directory, use Notepad (windows) or some text editor to create a simple text file with .cal as the ending, place in that directory.  Then access by Ctrl-F1.
 

I guess I'm missing something... If you go to Edit | Select | By Filter and then carefully craft the range of note velocities you want changed (eg. from 0 to 32), once they are selected you should be able to use Scale Velocity to set or adjust as needed. Either as specific values or percentages of the source.
 
Yes, a script would work but seems to be a bit of overkill.

brundlefly
Just noticed you are using S7. Back then, Process > Find/Change was Edit > Interpolate.
 
Note that 'Gain' on MIDI tracks is actually Velocity Offset. This can be used to quickly increase the Velocity of a whole clip by a fixed amount. But selectively adjusting just the lower limit is a special case that requres more steps.
 

 
Not on mine, though Process > Interpolate brings up the same "Event Filter -- Search" screen as in Bristol's reply #1 above. OK, I do Ctrl-A and go to that screen and set it for notes of 0 to 90 velocity, because I want all of those to be set at 90. Before I screw it up again, exactly what do I do in the little Scale velocity popup to get that result -- no velocities less than 90, nothing above 90 affected by the change? 
 
Velocity offset sounds great for when I need it some other time. 
 
I think we're on to something here. Thanks for sticking with me, gang. [EDITED/CORRECTED]