My dissertation is about childhood obesity and I working in HVing years ago disliked it intensely
OP has made a very, very good point but has slightly missed the emphasis.
Global strategies for tackling obesity are: breastfeeding, encouraging a healthy diet and increasing physical activity.
HV have a massive role to play, not just promotion of breast feeding but development of an attitude in parents around healthy diet.
The emphasis on weight, in terms of number is away from that point yes... Other factors such as general condition of the baby should be more important but it's a confident practitioner and parent who ignores the charts....
What HV should be encouraging is the recognition and following of babies cues in terms of being hungry... When top-ups or 3-4hrly feeds start being routinely advised or are advised with no real clinical need then the natural ability to know when you are hungry / full starts to get lost and that instinct is protective against obesity.
It's more likely to happen for formula fed babies as you can encourage a bottle feed easier than a breast feed, they take greater quantities and you can offer more calorific / heavier feeds in that volume - formula does not cause obesity but some of the feeding practices around formula can be a factor. Hence why feeding on demand / feeding cues led for formula is advocated and why you are advised to stick to the first milks for the first year.
Early weaning is another huge issue and all I will say is the advice is 6 months - the most important evidence is that the gut is unable to manage gluten under 6 months and various other foods can be problematic. The ability to handle solids in the mouth comes at different times too and actually spotting that development is as important as their 'age'.
Do HVs know this? They should, there is absolutely no excuse for not knowing it. It's not a secret - I am not a health professional these days and I can access it.
However, do HVs apply their experience and individual assessment of the need in front of them to that knowledge - yes they do... and that's not wrong but HVs see a snapshot of a life and we perhaps need to remember that with babies that advice is good for that short period of time before they develop / change again...
So yes OP HV has a huge responsibility towards improving obesity and emphasis should be feeding practices NOT weight.