The ECB Governing Council member and Bundesbank chief said international lenders must still make an "unembellished and honest" assessment of the country's finances.
"Politicians have evidently decided to continue financing Greece," Weidmann was quoted as saying by German newspaper Rheinishe Post.
Asked if the report of the troika of lenders - the International Monetary Fund, European Commission and European Central Bank - on Greece could nonetheless be independent, Weidmann said this was problematic.
"How can you objectively assess the completion of a program, if you are too afraid of the consequences of a negative conclusion?" he said. "I am relying on the fact the troika will deliver both an unembellished and honest assessment of the situation in Greece before payments are delivered."
Weidmann said the ECB and national central banks within the euro zone had bought up a considerable amount of Greek debt and thereby become one of Greece's biggest creditors, but could not take a haircut on that debt.
"The central banks may not waive Greece's debt, that would be a direct transfer and therefore would be tantamount to a forbidden monetary financing of a state," he said.
ECB President Mario Draghi said earlier this week the ECB was unlikely to help Greece much further in its bailout because it was prohibited from providing direct aid.
Weidmann reiterated his criticism of the ECB's plan to buy up the debt of struggling euro zone states.
"I DID NOT THREATEN TO RESIGN"
"While strict conditionality has been agreed for the new government debt purchase program, it remains to be seen how binding this is," he said.
"Fundamentally, monetary policy must not end up in tow of fiscal policy. Experience shows that independence is decisive for a central bank to keep monetary value stable."
Weidmann denied reports that he had threatened to resign over the ECB's bond-buying plans: "I did not threaten to resign. When I took on this office, I knew what to expect. What would a resignation have brought?"
Asked if he felt abandoned by German Chancellor Angela Merkel, he said "no", saying that central banks and governments had different duties and interests.
Weidmann also said the euro would still exist in 10 years' time: "I am certain of this. Clearly there is the political will to keep the euro area as a whole."
Weidmann dismissed the calls of some German politicians for Germany to have higher voting rights in the ECB to better reflect its share of the ECB's risk burdens.
He said these calls had grown because of increased fears over the risks the ECB was taking on but that existing rules on voting rights were designed such that ECB policymakers did not pursue national interests.
"The right response is not to change voting rights but to return to a narrow definition of monetary policy."
The Bundesbank chief said the German government's goal to balance its budget in 2014 was sensible but could have been jeopardized by decisions made by Merkel's center-right coalition last Monday that went "in the opposite direction".
The coalition agreed to scrap an unpopular health surcharge and to introduce extra child benefits, hoping to bolster support in the countdown to elections next year.
(Reporting By Sarah Marsh; Editing by Pravin Char)