I done did made a spaceship maw!

Japt, 8 6 bytes

Takes input as an array of characters, outputs an array of strings.

£qYçÃê

Try it

---

Explanation

£          :Map each element at (0-based) index Y
 q         :  Join input with
  Yç       :   Space repeated Y times
    Ã      :End Map
     ê     :Palindromise

---

Original, 8 bytes

I/O is a string. Uses the -R flag. Includes trailing spaces on each line.

¬£múYÄÃê

Try it

Explanation

             :Implicit input of string U
¬            :Split
 £           :Map each character at 0-based index Y
  m          :  Map original U
   ú         :    Right pad with spaces to length ...
    YÄ       :     Y+1
      Ã      :End map
       ê     :Palindromise
             :Implicitly join with newlines

R, 105 99 85 84 79 bytes

-6 thanks to @Kevin Cruissen and @Giuseppe

-14 from changing to a regex based method

-1 thanks to @Giuseppe

-5 thanks to @digEmALl

function(w,n=nchar(w)-1)write(trimws(Map(gsub,"",strrep(" ",n-abs(n:-n)),w)),1)

Try it online!

05AB1E, 10 9 bytes

Saved 1 bytes thanks to Adnan

εINð×ý}û»

Try it online!

Explanation

ε            # apply to each in input
 I           # push the input
  Nð×        # push <index> spaces
     ý       # merge the input on the spaces
      }      # end loop
       û     # palendromize
        »    # join on newlines