I just tried put some of that sticky patch tape on a hole in the ceiling and when I put jointing compund on it, the weight pulls the tape down.
What's the best way to repair ceiling holes in drywall?

 

Paper tape has a better track record than the 'sticky' tape. With paper tape you apply a thin layer of joint compound [the glue] and then press the tape into the mud and remove the excess j/c. What you are probably doing with your sticky tape is applying too much and the weight of it is pulling the tape loose. The 1st coat needs to be thin and let it dry before applying the 2nd.

 

It's a 6x6inch hole though - I thought the tape was only a couple cms wide?

 

I didn't know the hole was that big

There are 2 ways to repair a hole that size. 1st you want to insert a strip of wood about 9"-10" long and screw the ends to the drywall on each side of the hole. You will screw the patch piece of drywall to this strip of wood. You can either cut the drywall 2"-3" larger then the hole and then cut the backside of the patch piece the same size or slightly smaller than the hole leaving the paper face oversized. Then mud around the hole, insert the drywall and secure with a screw and press the excess paper into the mud like you would tape. Or you can cut the drywall to size, screw in place and then tape the perimeter.

Is the ceiling textured?

 

No texture,no.
They have patch squares that come in 6x6 or 7x7 but even with a thin layer that might hang down or will the jointing compund eventually firm up?
Could I also put a strip of 1x2 or 1x3 above the drywall and attach new piece of dry wall to that and then put tape around the small gaps?

 

It is difficult to make fiberglass or paper patch that size. You'd have to go at it slow and even then it's iffy.
A 1x2 secured above the hole is likely the best method to patch it. You either have to tape the perimeter or over cut the face paper on the drywall patch and use it in place of tape.

 

I've never liked the pre-made patches you can buy. I add 1x2 behind the existing rock for structure and screw in a new piece of rock - sometimes you are better off cutting a new hole to make matching with your patch easier. The mud and (paper) tape the edges just like any other joints.