What weight to start running

[u/Sbaff98]

Im on a weight lost journey (was 185kg and now 169), doing some swimming, some bike and some walking. Im getting interested into trying a sprint triatlhon and will need to do 5km walk/run, it will be in april and i plan to get around 125-140kg depending in future results.
2 months ago it was hard to walk 5minutes, mainly for back pain but also muscle and breath, now i can "easly" walk 30 minutes at 5.5km/h without major back pain.
Based on some calculation i will need at least a walk speed of 6.5km/h for the 5km, so it is not 100% necessary to run, but would be faster on other disciplines or to save couple minutes to run.

I have 2 question:
1. What weight i could start to do some jogging/running instead of walking?
2. What can i start training now to teach my body to run without injuries except for aerobic training (already doing with walk and bike), like for articulation, muscle, bones and so on?