Yes, 20kg is a lot Quim - I am not looking forward to it! The principle behind fixing tendons is that you need to apply increasing levels of load to them to strengthen them, but in a controlled manner so you don't aggravate them. What I do is put the weight into a backpack, then stand on tiptoes, shift all my weight onto the bad side (so standing on tiptoes on one leg only), and slowly lower back down on that single leg, back down the the floor. 3 sets of 15 reps at the weight I'm using now, every other day.
If I only wanted to walk or do low impact exercise, I would be fixed already (and I have been for over 6 months), but because I want to run, I need to add much higher amount of weight, to strengthen the tendon ready for the force it will have to deal with when I start running on it, every time my foot hits the ground. My physio reckons 20kg will do it - but they the time I am at that sort of weight, it'll only be 8 reps, not 15.
Losing weight will really help all this - my achilles won't be having to cope with quite for much force as I lumber around parkrun of a Saturday! And obviously running would also help with the weight loss, so it would be a win all round if/when I sort it. I don't really want to get my hopes up too much though - I am close to 2 years since the injury first happened, so it's been going on a LONG time. Tendons are stubborn bastards!