A Fix?
You could fix this by changing code.

   IF TYPE = '1' OR TYPE = '01' THEN ...  
... lines ommitted  
   ELSE IF TYPE = '2' OR TYPE = '02' THEN ...

Not too bad in this case but what if TYPE was a 3 or 4 character variable? What if TYPE could have 20 discrete values rather than just two. The possibilities quickly get unwieldy.
In general, it is probably better to go with the change of code below.

DATA MIXED;  
   INPUT @20 TYPE 2. @;  
   IF TYPE = 1 THEN  
      INPUT ID     1-3  
            AGE    4-5  
            WEIGHT 6-8;  
   ELSE IF TYPE = 2 THEN  
      INPUT ID     1-3  
            AGE    10-11  
            WEIGHT 15-17;  
DATALINES;  
00134168           1  
00245155            1  
003      23   220  2  
00467180           01  
005      35   190  02  
;

This code works just fine. TYPE is numeric so even though the characters that are read in the last data line are 02, the value that is stored internally is 2.