What did the original contract stipulate with regards to the payment date?
I would suggest that you try and accommodate their request, and be understanding and wait the 2 weeks.
I would however advise you to make an addendum to the original contract, agreeing to the slight delay in payment, but explicitly naming a date that payment must then be made in full, otherwise you reserve the right to invoke the late payment clause in the contract. Then ensure that both yourself and the client sign and date this addendum, and that both of you keep original copies of the revised contract.
2 weeks isn't an especially long time to wait for payment (I for example request that payment be made within 28 days of sign off or the 28th of the month, whichever is longest.), though I appreciate if it was specified in the original contract that payment should be made on completion then it is somewhat inconvenient for you for them to then request a delay in making payment.
Your options are of course somewhat limited because the period of 2 weeks isn't an especially substantial one, meaning that if you wrote to them requesting/demanding immediate payment, you'd still have to allow a period of 7 days for payment to be made after the date of receipt of the letter, this obviously does not include the 2-3 days it'll take to deliver your letter, or the 2-3 days it'll take for theirs to be delivered, nor the 3-5 business days a cheque would take to clear, which would almost certainly exceed the original 2 week timeframe that your client has offered to make payment in anyway.
Alternatively you could instruct your solicitor to write a formal letter to them requesting immediate payment, but again that is unlikely to provoke a response not to mention payment within those 2 weeks as offered by your client.
And in both the cases above, you'll do nothing other than likely lose them as a future client (and potential referrals that client may provide in the future) and potentially damage your reputation.
However, I do get the impression that you're a freelancer, in which case, I cannot stress the importance of implementing a robust structure for maintaining cash flow to assist you in situations such as these.
Hope that helps you a little.
G