What do you mean: "without the influence to match it"? The UK has always been incredibly influential in the EU. A lot of the things the EU implemented, were things the UK wanted.
Well that is subjective, but traditionally the leaders have been France and Germany and there has been an animus against the UK and its interests.
Then if you break it down, there is the question of eurosceptics. Where is their influence? Have they ever successfully reigned in the EU or got it to reverse anything? They are represented in the parliament but it is a toothless/show organisation.
Well, the EU was founded specifically around France and Germany. The UK did not want to join originally. They only joined later, and were for a long time considered the third most important and influential member, before Italy.
Then if you break it down, there is the question of eurosceptics. Where is their influence? Have they ever successfully reigned in the EU or got it to reverse anything? They are represented in the parliament but it is a toothless/show organisation.