It's fine to offer, but make sure you consider what you'll do if they refuse. That will show you how much (value wise) the house means to you. If they refuse and you'll still pay what your paying, then you need to accept that this is it's worth to you even though its overpriced.
When we moved, the buyer asked us to drop by £25k. We know they overpaid for ours by around that much - but they offered, so it was worth that much to them.
Anyway, we refused. What our buyers didn't know is that the seller we were buying from was being a dick and we'd reached the limit of our patience so didn't care if our buyer pulled out.
On the basis that we were so definite - we will not budge, the price is take it or leave it, they tried offering £25k drop, £15k, £10k, £5k - we just kept saying no. They even asked for £3k, which was laughable. At that point we told the EA that if they come back to us again for a discount, we are pulling out.
In the end, they paid thr full amount we offered, our seller continued to be a dick but we did all eventually complete.
The bottom line is, they over paid but the wanted the house. So therefore they didn't really overpay because it was worth that much to them.