can you post a video? post it to youtube and put the link on here
are you sure it is blood and not porphyrin?
http://ratguide.com/health/eyes/porphyrin_secretions_red_tears.php
Is he dehydrated? - dehydration kills (make sure he is getting lots of fluid - you can feed foods containing a lot of water such as watermelon, organic soy infant formula thickened with baby cereal, his rat blocks soaked in cool water to make mush, mixed greens, baby kale, peas, cooked sweet potato, cooked squash etc) - make sure he has a water dish that can not be upset, in addition to at least one water bottle.
http://ratguide.com/reference/ratmedhelp.pdf#search=dehydration
Is it possible that he is weak because he is not getting enough food?
Rat blocks soaked in cool water to make mush are easier to eat
and organic soy infant formula thickened with baby cereal cis easier to eat as well, and can also be licked off your finger or be given by syringe (no needle) one drop at a time into the side of the mouth (so it does not go down into his lungs)
Have you checked his teeth to make sure the front teeth are properly aligned?
http://ratguide.com/health/digestive/malocclusion.php
Is eating his food sideways something new?
What does it look like? video?
Does he have a head tilt? If so, how long has he had it?
What is his breathing like? laboured? requiring effort
Hold him up to your ear ad listen to both sides of his chest
If you think he is ill then he needs to see a good vet with the knowledge and experience to treat rats asap.
btw another place to post a medical concern is the facebook group Real Rat Lovers Want To Know