PHP, 129 Bytes

12 Bytes saved by @Titus Thank You

string = $argv[1],ratio = $argv[2], direction = $argv[3] inward = 0 ,Outward =1

for($i=0;$i+1<2*$l=strlen($t=($x=$argv)[1]);)echo$i%2?str_pad("",$x[2]*abs($x[3]*(0^$l/2+1)-($i++>=$l?$l-$i/2:$i/2))):$t[$i++/2];

Racket 348 bytes

(define(f s)(let*((c #\space)(sp(λ(l)(define ol'())(for((i(length l)))(for((j i))
(set! ol(cons c ol)))(set! ol(cons(list-ref l i)ol)))(for((n(floor(/(length l)2))))
(set! ol(cons c ol)))ol))(m(floor(/(string-length s)2)))(s1(sp(string->list(substring s 0 m)
)))(s2(sp(reverse(string->list(substring s m))))))(list->string(append(reverse s1)s2))))

Ungolfed:

(define(f s)
  (let* ((c #\space)
         (sp (λ (l)           ; subfn to add increasing spaces to list of characters
               (define ol '())
               (for ((i (length l)))
                 (for ((j i))
                   (set! ol (cons c ol)))
                 (set! ol (cons (list-ref l i)ol)))
               (for ((n (floor(/ (length l)2)))) 
                 (set! ol (cons c ol)))
               ol))
         (m (floor (/ (string-length s) 2)))                 ; find midpoint
         (s1 (sp (string->list (substring s 0 m))))          ; add spaces to first part
         (s2 (sp (reverse (string->list (substring s m)))))) ; add spaces to second part
    (list->string (append (reverse s1) s2))                  ; re-combine 2 parts
    ))

Testing:

(f "INTERSTELLAR")

Output:

"I N  T   E    R     S      T     E    L   L  A R"

MATL, 31 bytes

nq:tPvX<i?tX>Qw-]*kQ1whYs''1Gb(

Inputs are: string; 0 or 1 for inward or outward increasing; multiplier.

Try it online!

Explanation

Consider inputs 'INTERSTELLAR', 1, 0.5 as an example.

nq:    % Input string implicitly. Push [1 2 ... N-1] where N is the string length
       %   STACK: [1 2 3 4 5 6 7 8 9 10 11]
tP     % Duplicate, reverse
       %   STACK: [1 2 3 4 5 6 7 8 9 10 11], [11 10 9 8 7 6 5 4 3 2 1]
vX<    % Vertically concatenate. Minimum of each column
       %   STACK: [1 2 3 4 5 6 5 4 3 2 1]
i      % Input direction flag
       %   STACK: [1 2 3 4 5 6 5 4 3 2 1], 1
?      % If input flag was 1 (meaning outward increasing)
  tX>  %   Duplicate. Maximum
       %     STACK: [1 2 3 4 5 6 5 4 3 2 1], 6
  Q    %   Add 1
       %     STACK: [1 2 3 4 5 6 5 4 3 2 1], 7
  w-   %   Swap. Subtract
       %     STACK: [6 5 4 3 2 1 2 3 4 5 6]
]      % End
*k     % Input multiplier implicitly. Multiply. Round down
       %   STACK: [3 2 2 1 1 0 1 1 2 2 3]
Q      % Add 1
       %   STACK: [4 3 3 2 2 1 2 2 3 3 4]
1wh    % Prepend a 1
       %   STACK: [1 4 3 3 2 2 1 2 2 3 3 4]
Ys     % Cumulative sum
       %   STACK: [1  5  8 11 13 15 16 18 20 23 26 30]
''     % Push empty string
       %   STACK: [1  5  8 11 13 15 16 18 20 23 26 30], ''
1G     % Push input string again
       %   STACK: [1  5  8 11 13 15 16 18 20 23 26 30], '', 'INTERSTELLAR'
b      % Bubble up
       %   STACK: '', 'INTERSTELLAR', [1  5  8 11 13 15 16 18 20 23 26 30]
(      % Assign the characters from the top string into the empty string at the 
       % given positions. Intermediate positions are filled with character 0, 
       % which is displayed as a space
       %   STACK: 'I   N  T  E R ST E L  L  A   R'
       % Dispaly implicitly

05AB1E, 33 bytes

Uses CP-1252 encoding.

Gap multiplier is taken as negative when outwards increasing.

g;>Î.S<_²**ÄU¹vyð²¹g<;N.S*X+DUï×J

Try it online!

APL, 40 bytes

{⍵\⍨0~⍨∊1,⍨1,¨-⌊⍺×(1+⌈/-+)⍣⍺⍺(⌽⌊+)⍳⍴1↓⍵}

This takes the string as its right argument, the ratio as its left argument and the direction as its left operand (0 for inward and 1 for outward).

      1 (0 {⍵\⍨0~⍨∊1,⍨1,¨-⌊⍺×(1+⌈/-+)⍣⍺⍺(⌽⌊+)⍳⍴1↓⍵}) 'INTERSTELLAR'
I N  T   E    R     S      T     E    L   L  A R
      0.5 (0 {⍵\⍨0~⍨∊1,⍨1,¨-⌊⍺×(1+⌈/-+)⍣⍺⍺(⌽⌊+)⍳⍴1↓⍵}) 'INTERSTELLAR'
IN T E  R  S   T  E  L L AR
      2 (1 {⍵\⍨0~⍨∊1,⍨1,¨-⌊⍺×(1+⌈/-+)⍣⍺⍺(⌽⌊+)⍳⍴1↓⍵}) 'CODEGOLF'
C        O      D    E  G    O      L        F
      0.4 (1 {⍵\⍨0~⍨∊1,⍨1,¨-⌊⍺×(1+⌈/-+)⍣⍺⍺(⌽⌊+)⍳⍴1↓⍵}) 'CODEGOLF'
C O DEGO L F

Explanation:

• ⍳⍴1↓⍵: get a list of numbers from 1 to N-1, where N is the length of the string
• (⌽⌊+): invert the list, and at each position, get the lowest number of both lists (this gives the sizes of the gaps if increasing inwards)
• (1+⌈/-+)⍣⍺⍺: subtract each number in the list from the highest number in the list, and add 1. Do this ⍺⍺ times. (If ⍺⍺=0, nothing will happen, and if ⍺⍺=1, this will give the sizes of the gaps if increasing outwards.)
• -⌊⍺×: multiply each gap by ⍺, round it downwards, and negate it.
• ∊1,⍨1,¨: add a 1 in front of each gap, and a 1 at the very end of the list.
• 0~⍨: remove any zeroes.
• ⍵\⍨: use the resulting list to expand ⍵. Expand (\) works in the following manner: for each positive number, the current character is replicated that many times, and for each negative number, that many spaces are inserted, with the caveat that 0 and ¯1 do the same thing, which is why all the zeroes had to be removed earlier.

JavaScript (ES6), 86 82 81 80 bytes

Input is expected in currying syntax f(s)(r), with:

• s = string
• r = ratio + direction: a negative float for inward or a positive float for outward

let f =

s=>r=>s.replace(/./g,(c,i)=>c+' '.repeat(n+=i<l?-r:r),l=s.length/2,n=r>0&&l*r+r)

console.log(f("INTERSTELLAR")(-1));
console.log(f("INTERSTELLAR")(-0.5));
console.log(f("CODEGOLF")(2));
console.log(f("CODEGOLF")(0.4));