Checking to see if a string is letters + spaces ONLY?

use a regex. This one only matches if it starts with, contains, and ends with only letters and spaces.

^[ A-Za-z]+$

In Java, initialize this as a pattern and check if it matches your strings.

Pattern p = Pattern.compile("^[ A-Za-z]+$");
Matcher m = p.matcher("aaaaab");
boolean b = m.matches();

That isn't how you test character equality, one easy fix would be

public static boolean onlyLettersSpaces(String s){
  for(i=0;i<s.length();i++){
    char ch = s.charAt(i);
    if (Character.isLetter(ch) || ch == ' ') {
      continue;
    }
    return false;
  }
  return true;
}