@LBK thanks for the fast response!  Dr_Chrono_appointments__r is the relationship name between the accounts object (Parent) and the Appointments object (Child).

I inserted an account first as you recommaned but it didn't make any difference. Still 56% coverage..

I attached the v.2 below, please let me know how can I fix it.

P.S:

For the labs-object-based triggers I'm getting 100% coverage eventhough both appointments triggers and labs triggers follow the same logic and being affected by the same test class equally. (I'm going to attach the labs trigger code below at the end, it might help to figure out whats going on..)
 

@isTest
Private class InsertWeightToAppointment {

    @isTest static void InsertAppointment() {
        Account accnts = new Account();
        Appointments__c appt = new Appointments__c();
        Labs__c lb = new labs__c();
        
        accnts.name = 'afagas';
        accnts.RecordType = 'Patient';
        insert accnts;
        
        appt.weight__c = 200;
        appt.scheduled_time__c = date.today();
        appt.patient__c = '00161000013cLIg';
        appt.status__c = 'Completed';
        
        insert appt;
        
        lb.value__c = 100;
        lb.Specimen_Received__c = date.today();
        lb.patient__c = '00161000013cLIg';
        lb.Observation_Description__c = 'LDL';
        
        insert lb;
               
        
        }
        
    @isTest static void UpdateAppointment() {
        Appointments__c appt = new Appointments__c();
        Labs__c lb = new labs__c();
        appt.id = 'a0A6100000UUBeK';
        appt.weight__c = 100;
        appt.scheduled_time__c = date.today();
        appt.patient__c = '00161000013bPD9';
        
        update appt;   
        
        lb.value__c = 180;
        lb.Specimen_Received__c = date.today()-30;
        lb.patient__c = '00161000013cLIg';
        lb.Observation_Description__c = 'LDL';
        lb.id = 'a0E61000005Pg21';
        
        update lb;
        
        }
     
}

Labs trigger:
 

Trigger GetLatestLDLValue on labs__c(after insert, after update) {
    Set<Id> AccountIds = new Set<Id>();

    for (labs__c lb : trigger.new) {
        accountIds.add(lb.Patient__c);
    }

    //Elimnate the the accounts that don't have IDs for
    accountIds.remove(null);
    
//SOQL query that returns that initial weight value 
    if (!accountIds.isEmpty()) {
        List<Account> accountsToUpdate = new List<Account>(); 
        for (Account account : [
            SELECT Id,
                (
                    SELECT Specimen_Received__c, Value__c, Observation_description__c
                    From labs__r
                    WHERE Value__c != NULL AND Observation_description__c LIKE '%LDL%'
                    Order by Specimen_Received__c DESC
                    Limit 1
                )
            From Account
            Where Id in :accountIds
        ]) {
           
            //Declare a decimal variable to store initial labs value 
            Decimal LLDL = NULL;
            
            // Get(0) to return the first element in the list value
            if (!account.Labs__r.isEmpty()) {
                LLDL = account.labs__r.get(0).Value__c;
                
            }

            accountsToUpdate.add(new Account(
                Id = account.Id,
                Latest_LDL_labs_value__c = LLDL
            ));
            
        }   
        
        Update accountsToUpdate;
        
        }
      }