when you pronounce the phrase: "Sleep tight." do you stress both words equally? Is the 't' aspirated when the word "tight" is pronounced or it doesn't need to be aspirated?
Both words would be stressed here. The first /t/ in tight would be aspirated. The second would have no audible release in normal speech.
The /p/ will have no audible release either. It will be masked. By the time we release the /p/, the blockage for the /t/ will have already been formed and will be preventing all the air behind the tongue from leaving the mouth. The air released from the /t/ will have been been building up behind this blockage during the hold phase of the /t/. It is during this hold phase, not the /p/ one, that the air pressure in the mouth will be increasing for the powerful release of the plosive.