Well, you’re right, your neighbour has no right to spray weedkiller into your garden. There are few laws that specifically control this kind of behaviour so you have to fall back on the property based legal framework, as the garden is as much a part of your property as your houses is.
If you want to go down the legal route you can accuse her of criminal damage, an offence that carries a maximum prison sentence of three months with damages on top. The police are unlikely to be too keen to help out with something that they would consider a trivial matter though.
Make sure you write down the relevant events and take photographs of any damage. Write down the dates when you think she has sprayed weedkiller, and dates when you have spoken to her about it, for possible later use. You might find a sympathetic member of the police down at your local station who would be prepared to have an unofficial word with your neighbour if she carries on spraying.
What you do about this depends a lot on how important it is to have good neighbourly relations, as threatening her with police action isn’t likely to improve the situation. It might be better to try and reason with her and try to persuade her not to do it again.
Explain to her that although you understand that she feels justified, she ought to respect your desire not to use weedkiller. She is likely to push her point about the weeds but you must stick to your guns and explain that however strong her feelings are, she is simply not allowed to spray weedkiller on your property.
Threat of Legal Action
You could warn her that if she does it again you will take legal action, but it might be better to wait and see. If it does happen again, go through the process again but add that you will have no choice but to take legal action if there is a repeat. A visit from the police at this point might push the point home.
But if it continues you may then have to force the point with the police and insist they prosecute.