I understand English; I read and write English perfectly, but the accent won't go away. (Sofia Vergara)

“Sentence Stress” need not be referred to as the particular anxiety an ESL student experiences when attempting to pronounce a particularly wordy sentence in English…  Sentence Stress is actually the “music” of English, the thing that gives the language its particular “beat” or “rhythm”.  In general, in any given English utterance there will be particular words that carry more “weight” or “volume” (stress) than others.  From a speaking perspective, Sentence Stress will affect the degree to which an ESL student sounds “natural”.  In terms of listening, it affects how well a student can understand the utterances they hear. www.english raven.com

Sentence stress in English and all you need to know about sounding more English.