Lets not use the word "annoy". Russians know the reasons why India buys from US. Now the relationship is different, and is driven by mutual benefit.
We must not stand in the way if Russia wants to sell to Pakistan just as we would not stand in the way if Russia sells to Bangladesh or Sri Lanka. There is no benefit in using influence in blocking such sales.
The influence should be used for more worthwhile purposes.
I appreciate response also guidance and apologies for my long response:
My thinking was that we have look PRC how it deals with USA that has resulted in it being a huge massive manufacturing trillion dollar economy that disturbed the Russia stature in geo-political environment since 1970s and later dealings. PRC is able to dominate Russia in talks in many areas now.
One of the reasons for the above is because of USA economic corporation, consent and tolerance that have enabled PRC to grow economically exponentially. Further PRC has made huge inroads into Russia supply of military hardware by focusing on local production and in fact is trying to supply many of its customers. In overall scheme of things Russia and PRC are natural partners but that is not the case and lets not forget the (stealing) copying and unrecognition by PRC on its development to Russia.
Yet Russia deals militarily corporation with PRC (and one reason it needs to deal with India more exceedingly) and sometimes in areas that has allowed PRC to develop its own defense systems (be it through sometimes through approval, mistake and oversight).
Putin does not get impressed by having news reports to show he is macho inside PRC. He knows the facts. The other consideration is PRC and its relationship and use of Pakistan (a bit like North Korea).
Now we compare India and its relationship with Russia. If India is repeating what PRC did that is fine Russia can sell weapons to Pakistan. I am totally fine with that and we deserve it and we have backstabbed the Russians. But that is not the case and it is not a fact. India foreign policy and relationship with Russia is not such abstract and nonfigurative that makes Russia feel redundant and annoyed. In fact India foreign policy with USA is also not such abstract and nonfigurative and USA knows the parameters that we are dealing with and the application needs to be away from Russia and more to our neighbors.
India dealing with USA is an open relationship and is not anti-Russia for example compared to the PRC and USA pirouette that happened in such manner earlier. In fact one can redefine the India and USA relationship (focus on neighbors) to say that it will benefit Russia. The underlying basis has to be fairness to both USA and Russia in India. India is not going to dump USA suddenly also if they are better and best in some areas that has to be the fact. If Russia is better and best in some areas that has be continued.
I will go on to say that India has the right to veto sales of weapons to Pakistan by Russia since the Indo-Russia relationship is much more advanced and mature that people fail to realize. If Putin wants to dominate India that's fine but we have to keep repeating the reality. We have to also start comforting and helping and advising Russia and start behaving like a big(ger) power. It might not happen this time and it might.
Pakistan is a small market (unlike PRC where Russia can say to India) and selling helicopters and non-lethal weapons can be overlooked but doing strategic defense corporation and to the extreme having its entire air force being run on Russian engines is a separate matter (not sure if that is likely). If Russia is dealing with Pakistan (a nation that takes pride in defeating it in 1980s) in a much more close defense partnership it is purely for geo-political reason and is telling India that and not for economic and military sale reasons (it's a small market) which can be given to PRC. It would be a surprise to be honest and will not be because of India backstabbing Russia.
It is absolutely a different thing:
1) If Russia sells to Pakistan
2) If Russia sells to Bangladesh - Sri Lanka – militarily non-aggressive country to India
3) If Russia sells to PRC
Further India has not done anything against Russia interests and has not backstab them. India value the relationship with Russia and is not going to forget and disturb that. I am sure the actual situation is that the conversation is that India dealing more closely with USA will be good for Russia. If Russia wants to react because they are being treated badly that is not reality and India needs to deal with it. India has not treated Russia bad. It is different being open with a long trusted relationship that we have with the Russians.
The relationship with USA is good for Russia from one side it reduce and change PRC linear ascendancy (and history and connection it has with Russia) to the other extreme side that it helps in product improvement that can be shared and compared to Russia military hardware with purpose that it will improve and help Russian industry in the long-term.
If Russia deals with Pakistan the only country that benefits is PRC. It is like North Korea. If Russia supplies military hardware to North Korea the only benefit is PRC. Why and how this is being overshadowed by Indian getting closer with USA is moving away from the real discussion that needs to take place.
Russia relationship with PRC