The point of PCA is that your components are supposed to represent axes of principal variation. I.e. if you just use one principal component you can describe the most variation of true market movements with that, than you can with any other relative combinations of instruments.
So if your component (eigenvector) is:
[2y,5y,7y,10y] = ~[25,33,24,23], where I have used the ~ symbol to represent a normalisation opertion (the vector should really have norm equal to one), then the most common market-movement amidst your data is for 5y to be slightly more volatile than the other rates and 10y to be the least, but all swaps move in the same direction.
The point being that if you are considering a shock scenario described as "rates go higher by a considerable amount" then rather than saying [2y,5y,7y,10y]=[+25,+25,+25,+25] you can use the weights as determined by PCA which are more statistically likely (as measured from your historic dataset) to be representative of future market moves.
Indeed if I were tasked with this I would go one stage further. 25bps is an arbitrary choice of scenario, why have you chosen 25bps, why not 10 or 100 or 1bn? I would probably employ a statistical analysis over my historic dataset to see what is a reasonable scenario of stress given the distribution of factor multipliers that are applied to the dataset for any particular principal component.