What about something like this?  It may not be totally correct, but I think it'd be a starting point.  

Basically - I think you'll want to think in terms of child, parents, and grand parents.  You'll want to gather the parent Ids for the children that fired the trigger.  Then with those IDs, get and total all of the child for those parents.  Keep those totals in a map of <ParentId,Amount>.  Then you'll want to get all of the grandparents IDs from the parents.  Then get ALL of the parents using the grandparent IDs, building another map of <grandparentId,amount>.  With those two maps, get a LIST of accounts and update the Amt__c field.

Make sense?  It is a bit of a complicated process.
 

trigger totalAmount on Account (after update) {

  // Will need to use a Run Once technique so it doesn't get recursively called - I can post something on that if needed.

  // Get parents of accounts that fired the trigger
  set<id> parentIds = new set<id>();
  for(Account a :trigger.new) {
    if(a.ParentId != null) {
      parentIds.add(a.ParentId);
    }
  }

  // Get children of those parents & sum amount
  list<AggregateResult> childARs = [SELECT ParentId parentId, SUM(Amt__c) amtTotal
                                                           FROM Account
                                                           WHERE ParentId in :parentIds
                                                           GROUP BY parentId


  map<id,decimal> mParentAmounts = new map<id,decimal>();
  for (aggregateResult ar :childARs) {
    mParentAmounts.put(string.valueOf(ar.get('parentId')), decimal.valueOf(string.valueof(ar.get('amtTotal'))));
  }

  // Now get the Grandparent Ids
  list<Account> parents = new list<Account>([SELECT id,parentId FROM Account WHERE Id IN :mParentAmounts.keyset()]);
  set<id> grandParentIds = new set<id>();
  for(Account a :parents) {
    grandParentIds.add(a.parentId);
  }

  // Get all the children of the grandparents & sum totals, replacing the total in the mParentAmounts map
  list<Account> parents2 = new list<Account>([SELECT id,parentId,Amt__c FROM Account WHERE id IN :grandParentIds]);
  map<id,decimal> mGrandParentAmt = new map<id,decimal>();
  for(Account a :parents2) {
    decimal grandParentAmt = 0.00;
    if(mGrandParent.containsKey(a.parentId) {
      grandParentAmt = mGrandParent.get(a.parentId);
    }
    if(mParentAmounts.containsKey(a.id)) {
      grandParentAmt = grandParentAmt + mParentAmounts.get(a.id);    // Can't use the amt from the SOQL, as we just created a new amount for the parents
    } else {
      grandParentAmt = grandParentAmt + a.Amt__c;
    }
    mGrandParentAmt.put(a.parentId,grandParentAmt);
  }

// At this point we have two maps....
//     mParentAmounts and mGrandparentAmts  
//     Now, get those account records and update the amount
list<account> accountsToUpdate = new list<Account>([SELECT id,Amt__c FROM Account WHERE id IN :mParentsAmounts.keyset() OR id IN :mGrandparentsAmts.keyset()]);
for(Account a :accountsToUpdate) {
  if(mParentsAmounts.containsKey(a.id)) {
    a.Amt__c = mParentsAmounts.get(a.id);
  }
  if(mGrandparentsAmt.containsKey(a.id)) {
    a.Amt__c = mGrandparentsAmt.get(a.id);
  }
}

Update accountsToUpdate;   

}