Unfortunately there are a few little tricky parts about this. I've written something that should do the trick. You'll need to make a new class as well.

Trigger on opportunity:

trigger SyncCheckBoxOnOpportunity on Opportunity(after update) 
{
	OpportunitySyncUtil.syncLineItems(Trigger.new, Trigger.oldMap);
}

 Trigger on OpportunityLineItem (aka Opportunity Product):

trigger SyncCheckBoxOnOpportunityLineItem on OpportunityLineItem(after update)
{
	OpportunitySyncUtil.syncOpportunities(Trigger.new, Trigger.oldMap);
}

 Class:

public with sharing class OpportunitySyncUtil
{
	private static Boolean isSyncing = false;
	
	public static void syncLineItems(Opportunity[] newItems, Map<Id, Opportunity> oldItems)
	{
		//Prevent recursion
		if (!isSyncing)
		{
			isSyncing = true;
			
			Map<Id, Opportunity> opportunityMap = new Map<Id, Opportunity>{};
		
			for (Opportunity item : newItems)
			{
				if (item.Checkbox__c != oldItems.get(item.Id).Checkbox__c)
				{
					opportunityMap.put(item.Id, item);
				}
			}
			
			if (!opportunityMap.isEmpty())
			{
				OpportunityLineItem[] lineItemList = [ SELECT Id FROM OpportunityLineItem WHERE OpportunityId IN :opportunityMap.keySet() ];
				
				for (OpportunityLineItem item : lineItemList)
				{
					Opportunity o = opportunityMap.get(item.OpportunityId);
					item.Checkbox__c = o.Checkbox__c;
				}
				
				update lineItemList;
			}
		}		
	}
	
	public static void syncOpportunities(OpportunityLineItem[] newItems, Map<Id, OpportunityLineItem> oldItems)
	{
		//prevent recursion
		if (!isSyncing)
		{
			isSyncing = true;
			
			Map<Id, Opportunity> opportunityMap = new Map<Id, Opportunity>{};
		
			for (OpportunityLineItem item : newItems)
			{
				//It's changing from true to false
				if (item.Checkbox__c == false && oldItems.get(item.Id).Checkbox__c == true)
				{
					opportunityMap.put(item.OpportunityId, new Opportunity(Id=item.OpportunityId, Checkbox__c=false));
				}				
			}
			
			if (!opportunityMap.isEmpty())
			{
				update opportunityMap.values();
			}			
		}
	}
}

 This was written on the fly, so it may not compile immediately, change what you need. You'll also want to change the API Name of the checkbox to be whatever it needs to be.