Can anxiety cause a constant burning in pit of stomach for 3 weeks there all day?

Yes.: Anxiety can certainly cause this symptom which is worsened if accompanied by the decreased appetite of severe anxiety leading to unopposed gastric acidity.

Sure but...: ...There are lots of diseases of the stomach that can result in dyspepsia or pyrosis. These can be categorized as: problems with inflammation (e.g. Ulcers), with infection (e.g. H.Pylori or parasites), with motility (examples: gastroparesis, gastric outlet obstruction), with secretion (hyper or hypo-acidity), infiltrative (lymphoma, cancer), blood flow (gastropathies), functional dyspepsias, etc.