Regarding luggage weight limits, when in doubt, go based off what the airline's website says. So if their website says 20 kg limit per person per bag with no allowances larger than that, then you have to limit your stuff to 20 kg in one bag.

However, many airlines have over-weight fees and it varies depending on the airline. If your family members do not believe you, print it out right off of the airline's website and let them read it in black and white. :-) This is regarding checked luggage of course. There are usually different weight limits for carry-on luggage.

Heathrow's carry-on limits for liquids is the same as here in the US. If you go to Heathrow's website, they should have some good info there. Generally speaking, the rules are:

1. 100 ml limit per container
2. put all of your 100 ml liquid containers in a single quart-sized ziplock bag
3. things that are in a "wipe" form (like baby wipes) are exempt from this.
4. one quart-sized bag per ticketed passenger
5. larger quantities of liquids need to go in checked luggage or you have to throw it out.
6. when you go through security, you should remove the ziplock bag from your carry-on luggage so they can scan it seperately.