Focus on the key points
Grades are a means to the end, not the end goal, so you don't need to look at everything. It can be useful to have one or two key assessment criteria to look out for. What is the main reason you're asking students to do this?
This is especially useful for more complex assignments - especially things you'll be working through repeatedly, such as a lab report or an essay. Choose a couple of key elements to focus on. If it's the first essay of the term, you could look at format, and the introduction to help your class begin to master the structure and tone of the assignment, and use the rest of the essay as a chance for your class to practice - though maybe leave that out of your instructions!
As the term moves along, you can move focus on other areas, such as SPG or subject knowledge. This technique not only saves you lots of time, it actually can be useful for you as a teacher to break down what you're looking for from a class into small objectives, so you can see where more work is required, helping you to create a rubric that you can assess as you move through the term.
It can be beneficial for pupils too. Most will see their first attempt covered in corrections and come away feeling defeated. By strategically focusing on specific areas, your class will have a better opportunity to improve their skills over time.
Top tip: if you know particular students struggle with certain things, have a quick list of key skills you want to keep an eye on, to help ensure everyone is moving forward and making progress.
Keep things simple
Try to avoid complicated weighting or marking schemes … it can take longer to work out what marks you're giving (or worse, you realise you've been working it out wrong after you've done most of them!). If you're marking papers with weighting involved, it can be better to focus on how well the work meets the objectives, and leave the calculations out.
Get them to mark it!
This is nothing new, but asking your class to read each other's answers, or talk through responses as a class, shows how much their learning is moving forward. You could also your class to write a short paragraph of things they'd do differently, which means you get a great insight into how much each pupils is learning, and means you have a smaller amount of work to read through! You could try asking students to peer mark – that way you can quickly review the peer grades and catch anything that is immediately wrong.
This takes up class time, but may be worth it for some topics. If you're not quite convinced, imagine you've spent time teaching a new topic, and collect in homework, and find out that the whole class missed a key component and you need to re-teach the entire lesson. By discussing the homework as a class, you will discover gaps in understanding earlier, which is better for your class - and your sanity!
Build it into your lesson
Build in time periodically to help students on big projects or to give feedback on frequently used assignments, like lab reports or essays. Get the class working on something independently – and then call up pupils one at a time for a couple of minutes. Look over their work, identify one or two things they are doing well, and one or two things they could work on, and have them ask any questions they need to. Every student gets some one-on-one interaction with you and gets to hear you say something positive about her work. Even doing this exercise once or twice a term can help you get insight in each pupil's understanding, and it's a great way to coax shy pupils to ask the questions they need to further their learning.
Set up a schedule
Try to plan ahead when you have larger projects to mark and set time aside. However, if you're not realistic about how long you will need to spend marking, your work can pile up, even if you've set time aside, so it's important to be honest with yourself about what you can achieve in the time you have, otherwise you'll quickly feel stressed and get behind.
Sometimes there's no way to avoid it: you will have a mountain of work to mark. Hopefully, you'll know when those times are coming and be able to plan ahead. But before you hole up, plan something fun to look forward to, make it a part of your schedule and take it just as seriously as getting through your work. You'll be a happier person and a better teacher because of it.